What is the integral from 2 to 7 of xsqrt(x+2) ?

The integral from 2 to 7 of xsqrt(x+2) is 886/15

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integral from 2 to 7 of xsqrt(x+2)

\int_{2}^{7} x x + 2 d x

\frac{886}{15}

Solution steps

\int_{2}^{7} x x + 2 d x

Apply u-substitution

: \int_{4}^{9} (u - 2) u d u

= \int_{4}^{9} (u - 2) u d u

Expand

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

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

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

\int_{4}^{9} 2 u d u = \frac{76}{3}

= \frac{422}{5} - \frac{76}{3}

Simplify

\frac{422}{5} - \frac{76}{3} : \frac{886}{15}

= \frac{886}{15}

\int_{0}^{3} x^{2} + 1 d x

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

\int_{1}^{3} (x + 3)^{3} d x

\int_{- 3}^{0} x + 3 + 9 - x^{2} d x

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

What is the integral from 2 to 7 of xsqrt(x+2) ?
The integral from 2 to 7 of xsqrt(x+2) is 886/15