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

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

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

\int_{1}^{2} x^{3} \cdot 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_{0}^{a} 2 x - x^{2} d x

\int_{1}^{2} \frac{2 ^{x}}{x} d x

\int_{- 2 x}^{x} \frac{1}{csc ^{5} ( t )} d t

\int_{0}^{2} 5 x^{2} - 8 x + 4 d x

\int_{1}^{5} \frac{2}{t ^{3}} d t

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