What is the integral from 1 to 6 of x^4ln(x) ?

The integral from 1 to 6 of x^4ln(x) is -311+7776/5 ln(6)

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integral from 1 to 6 of x^4ln(x)

\int_{1}^{6} x^{4} ln (x) d x

- 311 + \frac{7776}{5} ln (6)

Decimal

2475.54432 \dots

Solution steps

\int_{1}^{6} x^{4} ln (x) d x

Apply Integration By Parts

: [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{6}

= [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{6}

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{1}^{6}

Compute the boundaries:

- 311 + \frac{7776}{5} ln (6)

= - 311 + \frac{7776}{5} ln (6)

\int_{0}^{\frac{y}{4}} e^{- y^{2}} d y

\int_{0}^{1} (3 - 2 x)^{- 2} d x

\int_{0}^{1} x^{2} \cdot e^{- 10 x} d x

\int_{1}^{\infty} \frac{1}{2 x + 9} d x

\int_{0}^{s i n (x)} t^{2} d t

What is the integral from 1 to 6 of x^4ln(x) ?
The integral from 1 to 6 of x^4ln(x) is -311+7776/5 ln(6)