What is the integral of (8x+15)ln(2x) ?

The integral of (8x+15)ln(2x) is 4x^2ln(2x)+15xln(2x)-2x^2-15x+C

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integral of (8x+15)ln(2x)

\int (8 x + 15) ln (2 x) d x

4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x + C

Solution steps

\int (8 x + 15) ln (2 x) d x

Apply Integration By Parts

= ln (2 x) (4 x^{2} + 15 x) - \int 4 x + 15 d x

\int 4 x + 15 d x = 2 x^{2} + 15 x

= ln (2 x) (4 x^{2} + 15 x) - (2 x^{2} + 15 x)

Simplify

ln (2 x) (4 x^{2} + 15 x) - (2 x^{2} + 15 x) : 4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x

= 4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x

Add a constant to the solution

= 4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x + C

What is the integral of (8x+15)ln(2x) ?
The integral of (8x+15)ln(2x) is 4x^2ln(2x)+15xln(2x)-2x^2-15x+C