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

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

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integral of 3^{sin(θ)}cos(θ)

\int 3^{s i n (θ)} cos (θ) d θ

\frac{3 ^{s i n (θ)}}{ln ( 3 )} + C

Solution steps

\int 3^{s i n (θ)} cos (θ) d θ

Apply u-substitution

: \int 3^{u} d u

= \int 3^{u} d u

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

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

Substitute back

u = sin (θ)

= \frac{3 ^{s i n (θ)}}{ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{s i n (θ)}}{ln ( 3 )} + C

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