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

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

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

\int sin (x) 2^{c o s (x)} d x

- \frac{2 ^{c o s (x)}}{ln ( 2 )} + C

Solution steps

\int sin (x) \cdot 2^{c o s (x)} d x

Apply u-substitution

: \int - 2^{u} d u

= \int - 2^{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int 2^{u} d u

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

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

Substitute back

u = cos (x)

= - \frac{2 ^{c o s (x)}}{ln ( 2 )}

Add a constant to the solution

= - \frac{2 ^{c o s (x)}}{ln ( 2 )} + C

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