What is the integral of (2x-1)ln(5x) ?

The integral of (2x-1)ln(5x) is x^2ln(5x)-xln(5x)-(x^2)/2+x+C

Popular >

integral of (2x-1)ln(5x)

\int (2 x - 1) ln (5 x) d x

x^{2} ln (5 x) - x ln (5 x) - \frac{x ^{2}}{2} + x + C

Solution steps

\int (2 x - 1) ln (5 x) d x

Apply Integration By Parts

: ln (5 x) (x^{2} - x) - \int x - 1 d x

= ln (5 x) (x^{2} - x) - \int x - 1 d x

\int x - 1 d x = \frac{x ^{2}}{2} - x

= ln (5 x) (x^{2} - x) - (\frac{x ^{2}}{2} - x)

Simplify

ln (5 x) (x^{2} - x) - (\frac{x ^{2}}{2} - x) : x^{2} ln (5 x) - x ln (5 x) - \frac{x ^{2}}{2} + x

= x^{2} ln (5 x) - x ln (5 x) - \frac{x ^{2}}{2} + x

Add a constant to the solution

= x^{2} ln (5 x) - x ln (5 x) - \frac{x ^{2}}{2} + x + C

\frac{d P}{d t} = P t

\int x^{4} ln (2 x) d x

\frac{d}{d x} (x^{2 a x})

f (b) = \frac{b}{z + n}

\int \frac{( 6 x ^{2} + 5 x + 6 )}{( x ^{2} + 1 ) ^{2}} d x

What is the integral of (2x-1)ln(5x) ?
The integral of (2x-1)ln(5x) is x^2ln(5x)-xln(5x)-(x^2)/2+x+C