What is the integral of 5^{sin(x)}*cos(x) ?

The integral of 5^{sin(x)}*cos(x) is (5^{sin(x)})/(ln(5))+C

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integral of 5^{sin(x)}*cos(x)

\int 5^{s i n (x)} \cdot cos (x) d x

\frac{5 ^{s i n (x)}}{ln ( 5 )} + C

Solution steps

\int 5^{s i n (x)} cos (x) d x

Apply u-substitution

= \int 5^{u} d u

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

= \frac{5 ^{u}}{ln ( 5 )}

Substitute back

u = sin (x)

= \frac{5 ^{s i n (x)}}{ln ( 5 )}

Add a constant to the solution

= \frac{5 ^{s i n (x)}}{ln ( 5 )} + C

What is the integral of 5^{sin(x)}*cos(x) ?
The integral of 5^{sin(x)}*cos(x) is (5^{sin(x)})/(ln(5))+C