What is the integral of 3^{ln(x)} ?

The integral of 3^{ln(x)} is 3^{ln(x)}x-1/(ln(3)+1)ln(3)x^{ln(3)+1}+C

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integral of 3^{ln(x)}

\int 3^{l n (x)} d x

3^{l n (x)} x - \frac{1}{ln ( 3 ) + 1} ln (3) x^{l n (3) + 1} + C

Solution steps

\int 3^{l n (x)} d x

Apply Integration By Parts

= 3^{l n (x)} x - \int ln (3) x^{l n (3)} d x

\int ln (3) x^{l n (3)} d x = \frac{1}{ln ( 3 ) + 1} ln (3) x^{l n (3) + 1}

= 3^{l n (x)} x - \frac{1}{ln ( 3 ) + 1} ln (3) x^{l n (3) + 1}

Add a constant to the solution

= 3^{l n (x)} x - \frac{1}{ln ( 3 ) + 1} ln (3) x^{l n (3) + 1} + C

What is the integral of 3^{ln(x)} ?
The integral of 3^{ln(x)} is 3^{ln(x)}x-1/(ln(3)+1)ln(3)x^{ln(3)+1}+C