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

The integral from 1 to 4 of x^3ln(x) is 128ln(2)-255/16

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integral from 1 to 4 of x^3ln(x)

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

128 ln (2) - \frac{255}{16}

Decimal Notation

72.78533 \dots

Solution steps

\int_{1}^{4} 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}^{4}

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

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

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

Compute the boundaries:

128 ln (2) - \frac{255}{16}

= 128 ln (2) - \frac{255}{16}

\int_{0}^{1} x^{3} \cdot e^{- x} d x

\int_{1}^{3} x^{3} e^{- \frac{5}{3} x} d x

\int_{- 1}^{1} x e^{- inπ x} d x

\int_{- \frac{π}{4}}^{\frac{π}{4}} tan (θ) d θ

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

What is the integral from 1 to 4 of x^3ln(x) ?
The integral from 1 to 4 of x^3ln(x) is 128ln(2)-255/16