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

The integral from 1 to 4 of x^{3/2}ln(x) is -124/25+128/5 ln(2)

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integral from 1 to 4 of x^{3/2}ln(x)

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

- \frac{124}{25} + \frac{128}{5} ln (2)

Decimal

12.78456 \dots

Solution steps

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

Apply Integration By Parts

: [\frac{2}{5} x^{\frac{5}{2}} ln (x) - \int \frac{2}{5} x^{\frac{3}{2}} d x]_{1}^{4}

= [\frac{2}{5} x^{\frac{5}{2}} ln (x) - \int \frac{2}{5} x^{\frac{3}{2}} d x]_{1}^{4}

\int \frac{2}{5} x^{\frac{3}{2}} d x = \frac{4}{25} x^{\frac{5}{2}}

= [\frac{2}{5} x^{\frac{5}{2}} ln (x) - \frac{4}{25} x^{\frac{5}{2}}]_{1}^{4}

Compute the boundaries:

- \frac{124}{25} + \frac{128}{5} ln (2)

= - \frac{124}{25} + \frac{128}{5} ln (2)

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

f (t) = 3 t

\int_{0}^{1} \frac{x}{( 3 x ^{2} + 1 ) ^{4}} d x

\int_{0}^{2 x} \frac{x y}{x ^{2} + y ^{2}} d y

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

What is the integral from 1 to 4 of x^{3/2}ln(x) ?
The integral from 1 to 4 of x^{3/2}ln(x) is -124/25+128/5 ln(2)