What is the integral from 1 to 10 of (ln^3(x))/x ?

The integral from 1 to 10 of (ln^3(x))/x is (ln^4(10))/4

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integral from 1 to 10 of (ln^3(x))/x

\int_{1}^{10} \frac{ln ^{3} ( x )}{x} d x

\frac{ln ^{4} ( 10 )}{4}

Decimal

7.02753 \dots

Solution steps

\int_{1}^{10} \frac{ln ^{3} ( x )}{x} d x

Apply u-substitution

: \int_{0}^{l n (10)} u^{3} d u

= \int_{0}^{l n (10)} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{0}^{l n (10)}

= [\frac{u ^{4}}{4}]_{0}^{l n (10)}

Compute the boundaries:

\frac{ln ^{4} ( 10 )}{4}

= \frac{ln ^{4} ( 10 )}{4}

\int_{2}^{10} 2 x - 4 d x

\int_{- \infty}^{4} 2 e^{x} d x

\int_{2}^{4} \frac{x}{x ^{2} + 3 x + 2} d x

\int_{0}^{3} \frac{x}{1 + 8 x ^{2}} d x

\int_{- π}^{π} 0 d x

What is the integral from 1 to 10 of (ln^3(x))/x ?
The integral from 1 to 10 of (ln^3(x))/x is (ln^4(10))/4