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

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

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

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

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

Solution steps

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

Apply u-substitution

= \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

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