What is the integral of s3^s ?

The integral of s3^s is (3^ss)/(ln(3))-(3^s)/(ln^2(3))+C

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integral of s3^s

\int s 3^{s} d s

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

Solution steps

\int s \cdot 3^{s} d s

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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What is the integral of s3^s ?
The integral of s3^s is (3^ss)/(ln(3))-(3^s)/(ln^2(3))+C