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

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

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

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

- \frac{1}{3 ln ^{3} ( 3 )} + \frac{1}{3 ln ^{3} ( 2 )}

Decimal

0.74953 \dots

Solution steps

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

Apply u-substitution

: \int_{l n (2)}^{l n (3)} \frac{1}{u ^{4}} d u

= \int_{l n (2)}^{l n (3)} \frac{1}{u ^{4}} d u

Apply the Power Rule

: [- \frac{1}{3 u ^{3}}]_{l n (2)}^{l n (3)}

= [- \frac{1}{3 u ^{3}}]_{l n (2)}^{l n (3)}

Compute the boundaries:

- \frac{1}{3 ln ^{3} ( 3 )} + \frac{1}{3 ln ^{3} ( 2 )}

= - \frac{1}{3 ln ^{3} ( 3 )} + \frac{1}{3 ln ^{3} ( 2 )}

\int_{2}^{3} 2^{2 x} d x

\int_{0}^{7} x e^{x^{2}} d x

\int_{- 1}^{2} x - (x^{2} - 2) d x

\int_{0}^{x} e^{t^{3}} d t

\int_{0}^{1} \frac{t}{t + 1} d t

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