What is the integral of za^z ?

The integral of za^z is (a^zz)/(ln(a))-(a^z)/(ln^2(a))+C

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integral of za^z

\int z a^{z} d z

\frac{a ^{z} z}{ln ( a )} - \frac{a ^{z}}{ln ^{2} ( a )} + C

Solution steps

\int z a^{z} d z

Apply Integration By Parts

: \frac{a ^{z} z}{ln ( a )} - \int \frac{a ^{z}}{ln ( a )} d z

= \frac{a ^{z} z}{ln ( a )} - \int \frac{a ^{z}}{ln ( a )} d z

\int \frac{a ^{z}}{ln ( a )} d z = \frac{a ^{z}}{ln ^{2} ( a )}

= \frac{a ^{z} z}{ln ( a )} - \frac{a ^{z}}{ln ^{2} ( a )}

Add a constant to the solution

= \frac{a ^{z} z}{ln ( a )} - \frac{a ^{z}}{ln ^{2} ( a )} + C

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What is the integral of za^z ?
The integral of za^z is (a^zz)/(ln(a))-(a^z)/(ln^2(a))+C