What is the integral of e^{x+sin(y)}cos(y) ?

The integral of e^{x+sin(y)}cos(y) is e^{sin(y)+x}+C

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integral of e^{x+sin(y)}cos(y)

\int e^{x + s i n (y)} cos (y) d y

e^{s i n (y) + x} + C

Solution steps

\int e^{x + s i n (y)} cos (y) d y

Apply u-substitution

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = sin (y) + x

= e^{s i n (y) + x}

Add a constant to the solution

= e^{s i n (y) + x} + C

What is the integral of e^{x+sin(y)}cos(y) ?
The integral of e^{x+sin(y)}cos(y) is e^{sin(y)+x}+C