What is the integral of 6/(xln^3(4x)) ?

The integral of 6/(xln^3(4x)) is -3/(ln^2(4x))+C

Popular >

integral of 6/(xln^3(4x))

\int \frac{6}{x ln ^{3} ( 4 x )} d x

- \frac{3}{ln ^{2} ( 4 x )} + C

Solution steps

\int \frac{6}{x ln ^{3} ( 4 x )} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{x ln ^{3} ( 4 x )} d x

Apply u-substitution

= 6 \cdot \int \frac{1}{u ln ^{3} ( u )} d u

Apply u-substitution

= 6 \cdot \int \frac{1}{v ^{3}} d v

Apply the Power Rule

= 6 (- \frac{1}{2 v ^{2}})

Substitute back

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

Simplify

6 (- \frac{1}{2 ln ^{2} ( 4 x )}) : - \frac{3}{ln ^{2} ( 4 x )}

= - \frac{3}{ln ^{2} ( 4 x )}

Add a constant to the solution

= - \frac{3}{ln ^{2} ( 4 x )} + C

\int 12 (x^{4} + 4 x^{2} + 1)^{2} (x^{3} + 2 x) d x

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

\int \frac{1}{6 x ^{3}} d x

\int 12 x^{11} d x

rr θ \cdot 2 - 4 sin (θ)

What is the integral of 6/(xln^3(4x)) ?
The integral of 6/(xln^3(4x)) is -3/(ln^2(4x))+C