What is the integral of 4^{ln(x)} ?

The integral of 4^{ln(x)} is 4^{ln(x)}x-2/(2ln(2)+1)ln(2)x^{2ln(2)+1}+C

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integral of 4^{ln(x)}

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

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

Solution steps

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

Apply Integration By Parts

: 4^{l n (x)} x - \int 2 ln (2) x^{2 l n (2)} d x

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

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

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

Add a constant to the solution

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

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 0

(1, 7), (10, 1)

\int sin (x) x d x

2 sin (x) + 2 x cos (x)

\int e^{y} cos (2 y) d y

What is the integral of 4^{ln(x)} ?
The integral of 4^{ln(x)} is 4^{ln(x)}x-2/(2ln(2)+1)ln(2)x^{2ln(2)+1}+C