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^{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

\int \frac{x - 1}{x ^{2} - 2 x + 5} d x

\int \frac{x - 1}{9 x ^{2} - 18 x + 17} d x

\int \frac{5 x}{9 - x ^{2}} d x

\int \frac{1}{2 x ^{2} - 8} d x

5^{x}

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