What is the integral of cos(x)2^{sin(x)} ?

The integral of cos(x)2^{sin(x)} is (2^{sin(x)})/(ln(2))+C

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integral of cos(x)2^{sin(x)}

\int cos (x) 2^{s i n (x)} d x

\frac{2 ^{s i n (x)}}{ln ( 2 )} + C

Solution steps

\int cos (x) \cdot 2^{s i n (x)} d x

Apply u-substitution

: \int 2^{u} d u

= \int 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = sin (x)

= \frac{2 ^{s i n (x)}}{ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{s i n (x)}}{ln ( 2 )} + C

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What is the integral of cos(x)2^{sin(x)} ?
The integral of cos(x)2^{sin(x)} is (2^{sin(x)})/(ln(2))+C