What is the integral of 6^{sin(x)}cos(x) ?

The integral of 6^{sin(x)}cos(x) is (6^{sin(x)})/(ln(6))+C

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integral of 6^{sin(x)}cos(x)

\int 6^{s i n (x)} cos (x) d x

\frac{6 ^{s i n (x)}}{ln ( 6 )} + C

Solution steps

\int 6^{s i n (x)} cos (x) d x

Apply u-substitution

: \int 6^{u} d u

= \int 6^{u} d u

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

= \frac{6 ^{u}}{ln ( 6 )}

Substitute back

u = sin (x)

= \frac{6 ^{s i n (x)}}{ln ( 6 )}

Add a constant to the solution

= \frac{6 ^{s i n (x)}}{ln ( 6 )} + C

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

\frac{d}{d x} (x^{- 1} (x^{2} + 1) x)

2 y^{^{''}} - 3 y^{^{'}} - 14 y = 0

\frac{d y}{d x} = 0.15 y + 200

(- x)^{^{'}}

What is the integral of 6^{sin(x)}cos(x) ?
The integral of 6^{sin(x)}cos(x) is (6^{sin(x)})/(ln(6))+C