What is the integral of 6xln(5x) ?

The integral of 6xln(5x) is 6(1/2 x^2ln(5x)-(x^2)/4)+C

Popular >

integral of 6xln(5x)

\int 6 x ln (5 x) d x

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

Solution steps

\int 6 x ln (5 x) d x

Take the constant out:

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

= 6 \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

= 6 (\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x)

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

= 6 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 6 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

y = x^{4} - 4 x^{2} + 4, y = x^{2}

f (x) = 2 x - x^{2}, (a, 0)

\frac{d}{d x} ((3 x^{2} + 1)^{40} (4 x - 7)^{50})

\int \frac{x}{27 + 6 x - x ^{2}} d x

tan^{40} (sec (cos (x)))

What is the integral of 6xln(5x) ?
The integral of 6xln(5x) is 6(1/2 x^2ln(5x)-(x^2)/4)+C