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)} \cdot 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 ln (\frac{x}{2}) d x

\int x e^{3 x + 1} d x

y = 4 x^{2}, y = 4

x \to 2 lim (- x^{2} + 4 x - 2)

\int \frac{9 x ^{3}}{x ^{2} + 1} d x

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