What is the integral from-1 to 4 of xsqrt(x+5) ?

The integral from-1 to 4 of xsqrt(x+5) is 316/15

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integral from-1 to 4 of xsqrt(x+5)

\int_{- 1}^{4} x x + 5 d x

\frac{316}{15}

Decimal

21.06666 \dots

Solution steps

\int_{- 1}^{4} x x + 5 d x

Apply u-substitution

= \int_{4}^{9} (u - 5) u d u

Expand

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

= \int_{4}^{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_{4}^{9} u^{\frac{3}{2}} d u - \int_{4}^{9} 5 u d u

\int_{4}^{9} u^{\frac{3}{2}} d u = \frac{422}{5}

\int_{4}^{9} 5 u d u = \frac{190}{3}

= \frac{422}{5} - \frac{190}{3}

Simplify

\frac{422}{5} - \frac{190}{3} : \frac{316}{15}

= \frac{316}{15}

What is the integral from-1 to 4 of xsqrt(x+5) ?
The integral from-1 to 4 of xsqrt(x+5) is 316/15