What is the integral of 8^{sin(θ)}cos(θ) ?

The integral of 8^{sin(θ)}cos(θ) is (8^{sin(θ)})/(3ln(2))+C

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integral of 8^{sin(θ)}cos(θ)

\int 8^{s i n (θ)} cos (θ) d θ

\frac{8 ^{s i n (θ)}}{3 ln ( 2 )} + C

Solution steps

\int 8^{s i n (θ)} cos (θ) d θ

Apply u-substitution

: \int 8^{u} d u

= \int 8^{u} d u

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

= \frac{8 ^{u}}{ln ( 8 )}

Substitute back

u = sin (θ)

= \frac{8 ^{s i n (θ)}}{ln ( 8 )}

Simplify

ln (8) : 3 ln (2)

= \frac{8 ^{s i n (θ)}}{3 ln ( 2 )}

Add a constant to the solution

= \frac{8 ^{s i n (θ)}}{3 ln ( 2 )} + C

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What is the integral of 8^{sin(θ)}cos(θ) ?
The integral of 8^{sin(θ)}cos(θ) is (8^{sin(θ)})/(3ln(2))+C