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

The integral from 1 to 2 of x^3ln(x) is 4ln(2)-15/16

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

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

4 ln (2) - \frac{15}{16}

Decimal

1.83508 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{1}^{2}

Compute the boundaries:

4 ln (2) - \frac{15}{16}

= 4 ln (2) - \frac{15}{16}

\int 2 sin (x) + 1 d x

\int_{0}^{\frac{π}{3}} (sec^{2} (x)) d x

y = sin (x cos (x))

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

\frac{\partial}{\partial x} (\frac{4 x}{5 + y})

What is the integral from 1 to 2 of x^3ln(x) ?
The integral from 1 to 2 of x^3ln(x) is 4ln(2)-15/16