What is the integral from 1 to 3 of ((ln^2(5))/(2x)) ?

The integral from 1 to 3 of ((ln^2(5))/(2x)) is (ln^2(5)ln(3))/2

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integral from 1 to 3 of ((ln^2(5))/(2x))

\int_{1}^{3} (\frac{ln ^{2} ( 5 )}{2 x}) d x

\frac{ln ^{2} ( 5 ) ln ( 3 )}{2}

Decimal Notation

1.42286 \dots

Solution steps

\int_{1}^{3} \frac{ln ^{2} ( 5 )}{2 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{ln ^{2} ( 5 )}{2} \cdot \int_{1}^{3} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{ln ^{2} ( 5 )}{2} [ln ∣ x ∣]_{1}^{3}

Compute the boundaries:

ln (3)

= \frac{ln ^{2} ( 5 )}{2} ln (3)

Simplify

= \frac{ln ^{2} ( 5 ) ln ( 3 )}{2}

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

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

\int_{0}^{1} x^{5} (1 - x^{2})^{\frac{3}{2}} d x

\int_{0}^{1} 2 t e^{- 2 t} d t

\int_{0}^{2} 1 + 5 t^{2} d t

What is the integral from 1 to 3 of ((ln^2(5))/(2x)) ?
The integral from 1 to 3 of ((ln^2(5))/(2x)) is (ln^2(5)ln(3))/2