Method choice.
AskSia recognizes which integration technique applies and explains why before applying it.
Method-aware
AI Solver by AskSia
Antiderivative Solver: the right method on each one
Type or photograph the function. AskSia tries the power rule first, then u-substitution, integration by parts, partial fractions, trig identities, or trig substitution as needed. The constant of integration is included automatically.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is an antiderivative?
An antiderivative of f(x) is a function F(x) whose derivative equals f(x). Every continuous function has infinitely many antiderivatives, differing only by a constant, which is why we write the indefinite integral as F(x) + C. To find an antiderivative, identify the function's structure and apply the matching technique: power rule for polynomials, u-substitution for compositions, integration by parts for products, partial fractions for rational functions, and trig identities for trig expressions.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Antiderivative.
Every step transparent, every answer self-checked.
U-substitution shown.
When substitution applies, AskSia names u, computes du, and rewrites the integral entirely in u before integrating.
Substitution
Integration by parts.
For products, AskSia picks u and dv via LIATE, applies the parts formula, and iterates if needed.
IBP
Partial fractions.
Rational functions get decomposed into simpler pieces, each of which integrates cleanly.
Partial fractions
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Antiderivative problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
Hi! What are we studying today?
Ask about your homework, lecture, or readings...↑
Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
☰
AskSia
+What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Antiderivative solver covers.
Power rule.
Antiderivative of x^n is x^(n+1)/(n+1). Direct for polynomials and roots.
Algebra
U-substitution.
Compositions like sin(x^2) * 2x. AskSia picks u = x^2.
Substitution
Integration by parts.
Products like x * e^x or x * sin(x). AskSia applies parts iteratively.
IBP
Partial fractions.
Rationals like 1/(x^2-1). Decompose and integrate each piece.
Rational
Trig integrals.
Powers of sin and cos, sqrt(a^2 - x^2). AskSia uses identities or trig substitution.
Trig
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
How does AskSia choose between substitution and parts?
Substitution applies when one part of the integrand is the derivative of another part. Integration by parts applies when the integrand is a product whose factors do not have a substitution relationship. AskSia scans for the substitution pattern first; if none exists, it tries integration by parts with the LIATE ordering for choosing u.
What is the LIATE rule?
LIATE stands for Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential. For integration by parts, the function class higher on the list becomes u (the part you differentiate). For example, in x * sin(x), Algebraic (x) is higher than Trig (sin x), so u = x. AskSia applies LIATE automatically.
Why is there a + C in the answer?
Because the antiderivative is not unique. If F(x) is one antiderivative of f(x), then F(x) + C is also an antiderivative for any constant C, since d/dx of a constant is 0. The + C captures all possible antiderivatives at once. For definite integrals, the + C cancels when you subtract.
Can AskSia handle nested compositions?
Yes. For something like sin(x^2 + 3x + 1) with the right kind of factor outside, AskSia identifies the inner function as u, computes du, and rewrites. If substitution does not clean things up, AskSia tries integration by parts or another technique. The choice is explained at each step.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
Start Today
Antiderivatives by the right method.
Join 2M+ students using AskSia to solve antiderivative problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
Let's Get in Touch
