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

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

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integral from 1 to 4 of (ln(x))/x

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

2 ln^{2} (2)

Decimal

0.96090 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{2 l n (2)} u d u

= \int_{0}^{2 l n (2)} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{2 l n (2)}

= [\frac{u ^{2}}{2}]_{0}^{2 l n (2)}

Compute the boundaries:

2 ln^{2} (2)

= 2 ln^{2} (2)

\int_{0}^{\frac{π}{2}} 2 x cos (x) d x

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

\int_{0}^{\frac{π}{6}} sin^{3} (x) d x

\int_{- 2}^{1} x^{4} + x^{3} - 2 x^{2} + 4 d x

\int_{- 2}^{2} x x^{2} + 1 d x

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