What is the integral from 0 to 4 of xsqrt(x+5) ?

The integral from 0 to 4 of xsqrt(x+5) is (108+100sqrt(5))/(15)

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integral from 0 to 4 of xsqrt(x+5)

\int_{0}^{4} x x + 5 d x

\frac{108 + 100 5}{15}

Decimal Notation

22.10711 \dots

Solution steps

\int_{0}^{4} x x + 5 d x

Apply u-substitution

: \int_{5}^{9} (u - 5) u d u

= \int_{5}^{9} (u - 5) u d u

Expand

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

= \int_{5}^{9} u^{\frac{3}{2}} - 5 u d u

Apply the Sum Rule:

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

= \int_{5}^{9} u^{\frac{3}{2}} d u - \int_{5}^{9} 5 u d u

\int_{5}^{9} u^{\frac{3}{2}} d u = \frac{486}{5} - 105

\int_{5}^{9} 5 u d u = 5 (18 - \frac{10 5}{3})

= \frac{486}{5} - 105 - 5 (18 - \frac{10 5}{3})

Simplify

\frac{486}{5} - 105 - 5 (18 - \frac{10 5}{3}) : \frac{108 + 100 5}{15}

= \frac{108 + 100 5}{15}

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What is the integral from 0 to 4 of xsqrt(x+5) ?
The integral from 0 to 4 of xsqrt(x+5) is (108+100sqrt(5))/(15)