What is the integral from 2 to 4 of 1/(x(ln(x))^3) ?

The integral from 2 to 4 of 1/(x(ln(x))^3) is 3/(8ln^2(2))

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integral from 2 to 4 of 1/(x(ln(x))^3)

\int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{3}} d x

\frac{3}{8 ln ^{2} ( 2 )}

Decimal Notation

0.78051 \dots

Solution steps

\int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{3}} d x

Apply u-substitution

: \int_{l n (2)}^{2 l n (2)} \frac{1}{u ^{3}} d u

= \int_{l n (2)}^{2 l n (2)} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{l n (2)}^{2 l n (2)}

= [- \frac{1}{2 u ^{2}}]_{l n (2)}^{2 l n (2)}

Compute the boundaries:

\frac{3}{8 ln ^{2} ( 2 )}

= \frac{3}{8 ln ^{2} ( 2 )}

\int_{- 4}^{3} \frac{1}{x ^{3}} d x

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\int_{1}^{4} \frac{x - 5}{x} d x

What is the integral from 2 to 4 of 1/(x(ln(x))^3) ?
The integral from 2 to 4 of 1/(x(ln(x))^3) is 3/(8ln^2(2))