What is the integral from 6 to 36 of 1/(x(ln(x))^8) ?

The integral from 6 to 36 of 1/(x(ln(x))^8) is (127)/(896ln^7(6))

Popular >

integral from 6 to 36 of 1/(x(ln(x))^8)

\int_{6}^{36} \frac{1}{x ( ln ( x ) ) ^{8}} d x

\frac{127}{896 ln ^{7} ( 6 )}

Decimal

0.00239 \dots

Solution steps

\int_{6}^{36} \frac{1}{x ( ln ( x ) ) ^{8}} d x

Apply u-substitution

: \int_{l n (6)}^{2 l n (6)} \frac{1}{u ^{8}} d u

= \int_{l n (6)}^{2 l n (6)} \frac{1}{u ^{8}} d u

Apply the Power Rule

: [- \frac{1}{7 u ^{7}}]_{l n (6)}^{2 l n (6)}

= [- \frac{1}{7 u ^{7}}]_{l n (6)}^{2 l n (6)}

Compute the boundaries:

\frac{127}{896 ln ^{7} ( 6 )}

= \frac{127}{896 ln ^{7} ( 6 )}

\int_{1}^{e^{x}} 9 ln (x) d x

\int_{3}^{5} \frac{1}{x - 4} d x

\int_{0}^{1} 5 x (1 - x)^{4} d x

\int_{0}^{1} a x + b d x

\int_{- 1}^{1} sec^{3} (x) tan^{3} (x) d x

What is the integral from 6 to 36 of 1/(x(ln(x))^8) ?
The integral from 6 to 36 of 1/(x(ln(x))^8) is (127)/(896ln^7(6))