What is the integral from 2 to 4 of-4x^3ln(x) ?

The integral from 2 to 4 of-4x^3ln(x) is -4(124ln(2)-15)

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integral from 2 to 4 of-4x^3ln(x)

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

- 4 (124 ln (2) - 15)

Decimal Notation

- 283.80100 \dots

Solution steps

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

Take the constant out:

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

= - 4 \cdot \int_{2}^{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]_{2}^{4}

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

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

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

Compute the boundaries:

124 ln (2) - 15

= - 4 (124 ln (2) - 15)

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

\int_{1}^{4} 2 x x^{2} + 1 d x

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

\int_{0}^{2} cos (x^{5}) d x

\int_{- 2}^{2} e^{2 x + 2} d x

What is the integral from 2 to 4 of-4x^3ln(x) ?
The integral from 2 to 4 of-4x^3ln(x) is -4(124ln(2)-15)