What is the integral of s5^s ?

The integral of s5^s is (5^ss)/(ln(5))-(5^s)/(ln^2(5))+C

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integral of s5^s

\int s 5^{s} d s

\frac{5 ^{s} s}{ln ( 5 )} - \frac{5 ^{s}}{ln ^{2} ( 5 )} + C

Solution steps

\int s \cdot 5^{s} d s

Apply Integration By Parts

: \frac{5 ^{s} s}{ln ( 5 )} - \int \frac{5 ^{s}}{ln ( 5 )} d s

= \frac{5 ^{s} s}{ln ( 5 )} - \int \frac{5 ^{s}}{ln ( 5 )} d s

\int \frac{5 ^{s}}{ln ( 5 )} d s = \frac{5 ^{s}}{ln ^{2} ( 5 )}

= \frac{5 ^{s} s}{ln ( 5 )} - \frac{5 ^{s}}{ln ^{2} ( 5 )}

Add a constant to the solution

= \frac{5 ^{s} s}{ln ( 5 )} - \frac{5 ^{s}}{ln ^{2} ( 5 )} + C

\frac{1}{x ^{3}}

sin (tan (2 x))

\frac{\partial}{\partial s} (2 s t)

y^{^{'}} = y (4 - y)

(ln (x))^{^{'}}

What is the integral of s5^s ?
The integral of s5^s is (5^ss)/(ln(5))-(5^s)/(ln^2(5))+C