MathSolverMathSolver.tools

Integral Calculator

Tip: drag a photo here or paste a screenshot (Ctrl+V)
How are solve allowances used?

Math, physics, chemistry and all AI tools share your plan allowance.

Each successful standard AI submission uses one standard solve. Deep reasoning uses one deep solve instead. Both count toward the daily solve limit.

Photos and selected PDF pages also use one daily photo solve per submission. Uploading a file or selecting a page does not start a solve. PDF upload requires Plus or Pro.

Local calculations, worked examples, hints, copying answers and cached answers use no solves.

Technical failures return the reserved solve. An automatic retry is included in the same submission. A new successful AI submission counts again, even if it follows an earlier answer.

Try:

Worked example

Step-by-step solution

∫xex dx\int x e^x \, dx

Step 1 / 4

Choose u and dv

u = x gets simpler when differentiated; e^x is easy to integrate.

u=x,  dv=ex dx  ⇒  du=dx,  v=exu = x,\; dv = e^x\,dx \;\Rightarrow\; du = dx,\; v = e^x

How to use the Integral Calculator

Enter an integral and this integral calculator names the technique it uses, works through every substitution, and checks the antiderivative by differentiating it back.

  1. Type the integral, for example “integral of x e^x dx”, or give bounds for a definite integral.
  2. Press Solve it. The calculator picks a technique: basic rules, u-substitution, integration by parts or partial fractions.
  3. Follow the substitution in each step and the + C on indefinite integrals.
  4. The last step differentiates the answer to confirm it.

Choosing an integration technique

∫u dv=uv−∫v du\int u\,dv = uv - \int v\,du

Start with the basic rules. If the integrand contains a function and its derivative, try u-substitution. If it is a product of two different kinds of functions, such as a polynomial times an exponential, integration by parts usually works.

For integration by parts, choose u to be the factor that gets simpler when differentiated. In ∫ x e^x dx, u = x becomes 1 while e^x stays easy to integrate.

Frequently asked questions

Can it evaluate definite integrals?

Yes. Give the bounds, for example “integral from 0 to 1 of x² dx”, and it finds the antiderivative and evaluates it exactly: 1/3.

Why is there a + C in the answer?

An indefinite integral is a family of antiderivatives that differ by a constant, because the derivative of any constant is zero.

What if an integral has no elementary antiderivative?

Some integrals, such as ∫ e^(−x²) dx, cannot be written with elementary functions. The calculator says so and, for definite integrals, gives a numerical value.

Related calculators

Have a different kind of math problem? Try the free math solver. Use the subject menu for physics and chemistry.