What is the integral of 4^{sin(x)}cos(x) ?

The integral of 4^{sin(x)}cos(x) is (2^{2sin(x)-1})/(ln(2))+C

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integral of 4^{sin(x)}cos(x)

\int 4^{s i n (x)} cos (x) d x

\frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )} + C

Solution steps

\int 4^{s i n (x)} cos (x) d x

Apply u-substitution

: \int 4^{u} d u

= \int 4^{u} d u

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

= \frac{4 ^{u}}{ln ( 4 )}

Substitute back

u = sin (x)

= \frac{4 ^{s i n (x)}}{ln ( 4 )}

Simplify

\frac{4 ^{s i n (x)}}{ln ( 4 )} : \frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )}

= \frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{2 s i n (x) - 1}}{ln ( 2 )} + C

x \to - 7 lim (\frac{x + 8}{x + 7})

\frac{d}{d x} (e^{x - 3})

2 x^{5}

\int e^{- 5 x} sin (x) d x

\frac{d}{d x} (\frac{- c x}{x ^{2} + y ^{2}})

What is the integral of 4^{sin(x)}cos(x) ?
The integral of 4^{sin(x)}cos(x) is (2^{2sin(x)-1})/(ln(2))+C