What is the integral from 1 to 2 of (5x^4-3)ln(x) ?

The integral from 1 to 2 of (5x^4-3)ln(x) is 26ln(2)-16/5

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integral from 1 to 2 of (5x^4-3)ln(x)

\int_{1}^{2} (5 x^{4} - 3) ln (x) d x

26 ln (2) - \frac{16}{5}

Decimal

14.82182 \dots

Solution steps

\int_{1}^{2} (5 x^{4} - 3) ln (x) d x

Expand

(5 x^{4} - 3) ln (x) : 5 x^{4} ln (x) - 3 ln (x)

= \int_{1}^{2} 5 x^{4} ln (x) - 3 ln (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} 5 x^{4} ln (x) d x - \int_{1}^{2} 3 ln (x) d x

\int_{1}^{2} 5 x^{4} ln (x) d x = - \frac{31}{5} + 32 ln (2)

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

= - \frac{31}{5} + 32 ln (2) - 3 (2 ln (2) - 1)

Simplify

- \frac{31}{5} + 32 ln (2) - 3 (2 ln (2) - 1) : 26 ln (2) - \frac{16}{5}

= 26 ln (2) - \frac{16}{5}

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What is the integral from 1 to 2 of (5x^4-3)ln(x) ?
The integral from 1 to 2 of (5x^4-3)ln(x) is 26ln(2)-16/5