What is the integral of ln^2(5x^3) ?

The integral of ln^2(5x^3) is x(ln(5)+3ln(x))^2-6(x(ln(5)+3ln(x))-3x)+C

Popular >

integral of ln^2(5x^3)

\int ln^{2} (5 x^{3}) d x

x (ln (5) + 3 ln (x))^{2} - 6 (x (ln (5) + 3 ln (x)) - 3 x) + C

Solution steps

\int ln^{2} (5 x^{3}) d x

Apply Integration By Parts

: x ln^{2} (5 x^{3}) - \int 6 ln (5 x^{3}) d x

= x ln^{2} (5 x^{3}) - \int 6 ln (5 x^{3}) d x

\int 6 ln (5 x^{3}) d x = 6 (x (ln (5) + 3 ln (x)) - 3 x)

= x ln^{2} (5 x^{3}) - 6 (x (ln (5) + 3 ln (x)) - 3 x)

Simplify

ln (5 x^{3}) : 3 ln (x) + ln (5)

= x (ln (5) + 3 ln (x))^{2} - 6 (x (ln (5) + 3 ln (x)) - 3 x)

Add a constant to the solution

= x (ln (5) + 3 ln (x))^{2} - 6 (x (ln (5) + 3 ln (x)) - 3 x) + C

\int (1 + 2 x)^{- 4} d x

\int e^{- y^{3}} d y

\int 100 + 210 x^{\frac{3}{4}} d x

\int \frac{( I n x ) ^{5}}{x} d x

\int \frac{( x + 5 )}{( x ^{2} - 6 x + 13 )} d x

What is the integral of ln^2(5x^3) ?
The integral of ln^2(5x^3) is x(ln(5)+3ln(x))^2-6(x(ln(5)+3ln(x))-3x)+C