What is the integral from 0 to 1 of 4x^3ln(x) ?

The integral from 0 to 1 of 4x^3ln(x) is -1/4

Popular >

integral from 0 to 1 of 4x^3ln(x)

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

- \frac{1}{4}

Decimal

- 0.25

Solution steps

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

Apply Integration By Parts

: [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{0}^{1}

= 4 [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{0}^{1}

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

= 4 [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{0}^{1}

Compute the boundaries:

- \frac{1}{16}

= 4 (- \frac{1}{16})

Simplify

= - \frac{1}{4}

\int_{1}^{4} x^{2} + 5 d x

\int_{- 2}^{3} e^{- t} d t

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

\int_{0}^{3} x^{2} + 4 d x

\int_{0}^{8} 1 + \frac{9}{4} x d x

What is the integral from 0 to 1 of 4x^3ln(x) ?
The integral from 0 to 1 of 4x^3ln(x) is -1/4