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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int a^{u} d u

= \int a^{u} d u

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

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (\frac{x}{yz})

\int (\frac{1}{1 + e ^{x}}) d x

x \to \infty lim (- e^{- a x})

\int \frac{x ^{2}}{5 + 2 x ^{3}} d x

\frac{\partial}{\partial x} (sin (2 x + 3 y))

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