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

= \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

y = (3 x - 4)^{5}

\frac{d}{d x} (ln (2 x + 1) - x^{2})

f (x) = csc^{2} (x)

\int_{1}^{2} \frac{11}{x ^{3} + 4 x} d x

2 cos^{2} (t)

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