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∫xex dx\int x e^x\,dx
01
Choose integration by partsu=xdv=ex dxu=x\qquad dv=e^x\,dx
02
Simplify and check(x−1)ex+C(x-1)e^x+C
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01

Your integral

∫(x ex) dx\int\left(x\,e^{x}\right)\,dx

Functions use radians. asin, acos and atan are inverse functions.

Use * for multiplication, ^ for powers and parentheses: sin(x), exp(x), log(x).

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02

Solution

∫xex dx\int x e^x\,dxGuided example
Exact result(x−1)ex+C(x-1)e^x+C
6 steps to understand it

  1. We have a product of an algebraic function and an exponential. Integration by parts simplifies the x factor when differentiated.

    Explain this step

    Read this stage and identify what changes and what remains constant. In a multiple integral, integrate the innermost variable first while treating the others as parameters. Check each transformation before moving on.

    I=∫xex dxI=\int x e^x\,dx

  2. Choose u = x because its derivative is 1, and dv = eˣ dx because its primitive is immediate.

    Explain this step

    Identify u, dv, du and v. Differentiating u should simplify the product. Substitute into uv − ∫v du and keep the minus sign; repeating parts may reduce a polynomial degree.

    u=x,dv=ex dx,du=dx,v=exu=x,\quad dv=e^x\,dx,\quad du=dx,\quad v=e^x
    Write u, dv, du and v before substituting.

  3. Apply the formula. The minus sign applies to the entire remaining integral.

    Explain this step

    Read this stage and identify what changes and what remains constant. In a multiple integral, integrate the innermost variable first while treating the others as parameters. Check each transformation before moving on.

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

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Learn to solve integrals, method by method

Start by identifying the integral type and the problem conditions. These guides explain when to choose each technique, show examples and highlight common mistakes.

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Integral calculator questions

How do I solve an integral step by step?

Enter the integrand, select the variable and specify bounds for a definite integral. Select a method or use automatic selection. Review each transformation and use differentiation to check an antiderivative. This check does not establish convergence of an improper integral.

How do I enter double and triple integrals?

Select Double or Triple, specify the order from inside out and enter each variable’s bounds. For polar, cylindrical or spherical coordinates, enter the original function in x, y, z: the calculator includes the Jacobian. Check that the bounds describe the intended region.

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Can it solve every integral?

Not every integral has an elementary solution. Some require special functions; others may remain unevaluated or exceed browser resources. The library also explains techniques the engine does not automate. Review conditions and consult guides before interpreting a result.

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