What is the integral of e^x(x+1)cos(xe^x) ?

The integral of e^x(x+1)cos(xe^x) is sin(xe^x)+C

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integral of e^x(x+1)cos(xe^x)

\int e^{x} (x + 1) cos (x e^{x}) d x

sin (x e^{x}) + C

Solution steps

\int e^{x} (x + 1) cos (x e^{x}) d x

Apply u-substitution

= \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= sin (u)

Substitute back

u = x e^{x}

= sin (x e^{x})

Add a constant to the solution

= sin (x e^{x}) + C

What is the integral of e^x(x+1)cos(xe^x) ?
The integral of e^x(x+1)cos(xe^x) is sin(xe^x)+C