What is the integral of s8^s ?

The integral of s8^s is (8^ss)/(3ln(2))-(8^s)/(9ln^2(2))+C

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integral of s8^s

\int s 8^{s} d s

\frac{8 ^{s} s}{3 ln ( 2 )} - \frac{8 ^{s}}{9 ln ^{2} ( 2 )} + C

Solution steps

\int s \cdot 8^{s} d s

Apply Integration By Parts

: \frac{8 ^{s} s}{3 ln ( 2 )} - \int \frac{8 ^{s}}{3 ln ( 2 )} d s

= \frac{8 ^{s} s}{3 ln ( 2 )} - \int \frac{8 ^{s}}{3 ln ( 2 )} d s

\int \frac{8 ^{s}}{3 ln ( 2 )} d s = \frac{8 ^{s}}{9 ln ^{2} ( 2 )}

= \frac{8 ^{s} s}{3 ln ( 2 )} - \frac{8 ^{s}}{9 ln ^{2} ( 2 )}

Add a constant to the solution

= \frac{8 ^{s} s}{3 ln ( 2 )} - \frac{8 ^{s}}{9 ln ^{2} ( 2 )} + C

\int \frac{x ^{2}}{x ^{2} + 2} d x

y = 3 - 6 x

\frac{\partial}{\partial x} (x^{2} cos (x))

y^{^{'}} + x y = 1

\int 1 + 2 sin (x) + sin^{2} (x) d x

What is the integral of s8^s ?
The integral of s8^s is (8^ss)/(3ln(2))-(8^s)/(9ln^2(2))+C