LIATE-based choice.
AskSia ranks the two factors by LIATE and picks u as the higher-ranked one, with the reasoning shown.
LIATE
AI Solver by AskSia
Integration by Parts Solver: the right u every time
Type or photograph the integral. AskSia picks u and dv using the LIATE rule, applies the parts formula, and iterates when the resulting integral still needs work. Tabular integration available for polynomial-times-exponential or polynomial-times-trig products.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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asksia.ai/solver
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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
When and how do you use integration by parts?
Integration by parts is the integration analogue of the product rule. The formula is the integral of u dv equals u*v minus the integral of v du. Use it when the integrand is a product of two functions of different types (algebraic and trig, polynomial and exponential, log and algebraic). The LIATE rule orders function classes (Logarithmic, Inverse trig, Algebraic, Trig, Exponential) and says: u should be the function class higher on the list.
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solution accuracy
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problems solved
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avg solve time
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study-ready explanations
Why AskSia Solver
Why students use AskSia for Integration by Parts.
Every step transparent, every answer self-checked.
Iterative application.
If the resulting integral still needs parts, AskSia applies it again with a fresh choice of u.
Iterative
Loop pattern recognition.
Integrals of e^x*cos(x) loop back. AskSia recognizes and solves algebraically.
Smart
Tabular integration.
For polynomial-times-(exp or trig), AskSia uses the tabular shortcut to save iterations.
Tabular
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 Integration by Parts 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
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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
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
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Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Integration by Parts solver covers.
x times exponential.
integral x*e^x dx. u = x, dv = e^x dx. AskSia applies parts cleanly.
Standard
x times trig.
integral x*sin(x) dx. AskSia chooses u and dv via LIATE.
Standard
Log times algebraic.
integral ln(x) * x dx. u = ln(x) by LIATE.
Log
Iterative parts.
integral x^2 * e^x dx requires two iterations. AskSia shows each.
Iterative
Loop integrals.
integral e^x * sin(x) dx. AskSia recognizes the loop and solves algebraically.
Loop
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 the LIATE rule work?
LIATE stands for Logarithmic, Inverse trig, Algebraic, Trig, Exponential. When choosing u, pick the factor whose class is higher on the list. So in integral x*e^x dx, Algebraic (x) ranks above Exponential (e^x), making u = x and dv = e^x dx. The LIATE choice typically simplifies the integral of v du.
When do I need to apply integration by parts more than once?
When the resulting integral after the first application is still a product needing parts. For example, integral x^2 * e^x dx requires two applications: the first reduces x^2 to 2x, the second reduces 2x to 2. After two iterations, the integral becomes elementary.
What is the loop pattern?
For integrals like integral e^x * cos(x) dx, applying parts twice produces the original integral on the right side with a coefficient. You can then solve algebraically for the integral. AskSia recognizes this pattern after the second parts application and sets up the algebraic equation.
Is tabular integration always faster?
It is faster when one factor is a polynomial that differentiates to zero (so the table terminates) and the other has an easy antiderivative pattern. For integral x^4 * sin(x) dx, tabular saves four applications of parts. AskSia uses tabular automatically when the integrand matches this pattern.
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.
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