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

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

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integral of e^xcos(e^x+1)

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

sin (e^{x} + 1) + C

Solution steps

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

Apply u-substitution

: \int cos (u + 1) d u

= \int cos (u + 1) d u

Apply u-substitution

: \int cos (v) d v

= \int cos (v) d v

Use the common integral:

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

= sin (v)

Substitute back

= sin (e^{x} + 1)

Add a constant to the solution

= sin (e^{x} + 1) + C

\int x (1 - x)^{4} d x

\int \frac{5 x ^{2} + 4}{x ^{3} + 4 x} d x

\int \frac{t ^{5} - 1}{t ^{4} - 1} d t

\int \frac{x}{9 + 8 x ^{2} - x ^{4}} d x

\int x - sin (x) d x

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