What is the integral of 7^{2ln(x)} ?

The integral of 7^{2ln(x)} is 49^{ln(x)}x-2/(2ln(7)+1)ln(7)x^{2ln(7)+1}+C

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integral of 7^{2ln(x)}

\int 7^{2 l n (x)} d x

4 9^{l n (x)} x - \frac{2}{2 ln ( 7 ) + 1} ln (7) x^{2 l n (7) + 1} + C

Solution steps

\int 7^{2 l n (x)} d x

Simplify

7^{2 l n (x)} : 4 9^{l n (x)}

= \int 4 9^{l n (x)} d x

Apply Integration By Parts

= 4 9^{l n (x)} x - \int 2 ln (7) x^{2 l n (7)} d x

\int 2 ln (7) x^{2 l n (7)} d x = \frac{2}{2 ln ( 7 ) + 1} ln (7) x^{2 l n (7) + 1}

= 4 9^{l n (x)} x - \frac{2}{2 ln ( 7 ) + 1} ln (7) x^{2 l n (7) + 1}

Add a constant to the solution

= 4 9^{l n (x)} x - \frac{2}{2 ln ( 7 ) + 1} ln (7) x^{2 l n (7) + 1} + C

What is the integral of 7^{2ln(x)} ?
The integral of 7^{2ln(x)} is 49^{ln(x)}x-2/(2ln(7)+1)ln(7)x^{2ln(7)+1}+C