What is the integral of 12xln(5x) ?

The integral of 12xln(5x) is 12(1/2 x^2ln(5x)-(x^2)/4)+C

Popular >

integral of 12xln(5x)

\int 12 x ln (5 x) d x

12 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

Solution steps

\int 12 x ln (5 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 12 \cdot \int x ln (5 x) d x

Apply Integration By Parts

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

= 12 (\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x)

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 12 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 12 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

x \to - 3 - lim (2 x^{2} - 6)

\int \frac{6 x ^{2} + x - 1}{3 x ^{3} - 9 x ^{2} + x - 3} d x

tan (e^{6 t}) + e^{t a n (6 t)}

\int - e^{2 t} + t e^{t} d t

\int_{0}^{1} x 6 - x^{2} d x

What is the integral of 12xln(5x) ?
The integral of 12xln(5x) is 12(1/2 x^2ln(5x)-(x^2)/4)+C