What is the integral from 1 to 3 of 5x^3ln(x) ?

The integral from 1 to 3 of 5x^3ln(x) is 5(-5+81/4 ln(3))

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integral from 1 to 3 of 5x^3ln(x)

\int_{1}^{3} 5 x^{3} ln (x) d x

5 (- 5 + \frac{81}{4} ln (3))

Decimal Notation

86.23449 \dots

Solution steps

\int_{1}^{3} 5 x^{3} ln (x) d x

Take the constant out:

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

= 5 \cdot \int_{1}^{3} 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}^{3}

= 5 [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{1}^{3}

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

= 5 [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{1}^{3}

Compute the boundaries:

- 5 + \frac{81}{4} ln (3)

= 5 (- 5 + \frac{81}{4} ln (3))

\int_{0}^{2} \frac{1}{16 - x ^{2}} d x

\frac{d}{d θ} (3 sin (2 θ))

n = 1 \sum \infty cos (4 n)

\frac{d}{d x} (a e^{a x})

\frac{d}{d x} ((x^{3} + 2 x - 7) (3 + x - x^{2}))

What is the integral from 1 to 3 of 5x^3ln(x) ?
The integral from 1 to 3 of 5x^3ln(x) is 5(-5+81/4 ln(3))