Table-first inversion.
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Inverse Laplace Solver
From F(s) back to f(t). Cleanly.
Type or photograph F(s). AskSia identifies the inverse with the standard Laplace table, applies partial fraction decomposition when F(s) is rational, and uses shift theorems for shifted or modulated factors. Convolution available for products that do not factor cleanly.
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
How do you compute an inverse Laplace transform?
To find the inverse Laplace transform of F(s), match F(s) to known table entries when possible. If F(s) is rational, decompose into partial fractions, then inverse-transform each piece. The first shift theorem handles e^(at)*f(t) patterns: if F(s-a) matches a table entry, the inverse is e^(at) times that table function. The second shift theorem handles delays. Convolution helps when F(s) is a product without a direct table entry.
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solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Laplace Inverse.
Every step transparent, every answer self-checked.
Partial fractions.
Rational F(s) decomposed into linear and quadratic pieces, each of which inverts using the table.
Partial fractions
Shift theorems.
First shift for F(s-a), second shift for e^(-as) factors (delays with step function).
Shifts
Convolution path.
When F(s) is a product without a clean table match, AskSia returns the convolution of inverses.
Convolution
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 Laplace Inverse 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
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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
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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
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Laplace Inverse solver covers.
Standard forms.
F(s) = 1/(s-3), s/(s^2+4), 1/s^n. Direct table inversion.
Table
Rational F(s).
Partial fractions decomposition, then invert each piece.
Partial fractions
Shifted exponential.
1/((s-2)^2+9) inverts to e^(2t) * sin(3t)/3 via first shift.
First shift
Delays.
e^(-2s)/s inverts to u(t-2), a delayed step function.
Second shift
ODE solutions.
After solving ODE in s, inverse-transform Y(s) to recover y(t).
ODE
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.
What is the first step in inverting a rational F(s)?
Factor the denominator and check whether F(s) matches a table entry directly. If not, perform partial fraction decomposition: write F(s) as a sum of simpler rational pieces, each of which is a known transform. The coefficients are found by clearing denominators and solving a linear system.
How does the second shift theorem work?
The Laplace transform of u(t-a) * f(t-a) is e^(-as) * F(s). Inversely, if you see e^(-as) * F(s), the inverse is u(t-a) * f(t-a), where f is the inverse of F. AskSia detects e^(-as) factors and applies the second shift theorem.
What about repeated factors in the denominator?
For repeated linear factors like (s-a)^n, partial fractions include terms A_1/(s-a) + A_2/(s-a)^2 + ... + A_n/(s-a)^n. Each piece inverts to a polynomial-times-exponential like t^(k-1) * e^(at) / (k-1)!. AskSia sets up the full decomposition correctly.
When does AskSia use convolution?
When F(s) is naturally a product G(s) * H(s) and neither G nor H has an obvious match. The inverse is then the convolution integral of g(t) and h(t). AskSia sets up the convolution and evaluates it when possible.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. 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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Inverse Laplace, the right method on each F(s).
Join 2M+ students using AskSia to solve laplace inverse problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
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