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

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

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

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

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

Solution steps

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

\int_{0}^{\frac{π}{4}} tan (x) d x

\frac{8}{3 s ^{2} + 12} + \frac{3}{s ^{2} - 49}

\int 1 + 64 x^{2} d x

\int e^{2} cos (x) d x

\frac{4}{s ^{4} + 4}

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