What is the integral of 3^{cos(x)}sin(x) ?

The integral of 3^{cos(x)}sin(x) is -(3^{cos(x)})/(ln(3))+C

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integral of 3^{cos(x)}sin(x)

\int 3^{c o s (x)} sin (x) d x

- \frac{3 ^{c o s (x)}}{ln ( 3 )} + C

Solution steps

\int 3^{c o s (x)} sin (x) d x

Apply u-substitution

= \int - 3^{u} d u

Take the constant out:

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

= - \int 3^{u} d u

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

= - \frac{3 ^{u}}{ln ( 3 )}

Substitute back

u = cos (x)

= - \frac{3 ^{c o s (x)}}{ln ( 3 )}

Add a constant to the solution

= - \frac{3 ^{c o s (x)}}{ln ( 3 )} + C

What is the integral of 3^{cos(x)}sin(x) ?
The integral of 3^{cos(x)}sin(x) is -(3^{cos(x)})/(ln(3))+C