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

The integral from 1 to 4 of sqrt(x)(5x-3) is 48

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integral from 1 to 4 of sqrt(x)(5x-3)

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

48

Solution steps

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

Expand

x (5 x - 3) : 5 x^{\frac{3}{2}} - 3 x

= \int_{1}^{4} 5 x^{\frac{3}{2}} - 3 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}^{4} 5 x^{\frac{3}{2}} d x - \int_{1}^{4} 3 x d x

\int_{1}^{4} 5 x^{\frac{3}{2}} d x = 62

\int_{1}^{4} 3 x d x = 14

= 62 - 14

Simplify

= 48

\int_{0}^{4} \frac{x ^{2}}{x + 1} d x

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What is the integral from 1 to 4 of sqrt(x)(5x-3) ?
The integral from 1 to 4 of sqrt(x)(5x-3) is 48