What is the integral from 1 to 6 of xsqrt(x+3) ?

The integral from 1 to 6 of xsqrt(x+3) is 232/5

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integral from 1 to 6 of xsqrt(x+3)

\int_{1}^{6} x x + 3 d x

\frac{232}{5}

Decimal

46.4

Solution steps

\int_{1}^{6} x x + 3 d x

Apply u-substitution

= \int_{4}^{9} (u - 3) u d u

Expand

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

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

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

\int_{4}^{9} 3 u d u = 38

= \frac{422}{5} - 38

Simplify

\frac{422}{5} - 38 : \frac{232}{5}

= \frac{232}{5}

What is the integral from 1 to 6 of xsqrt(x+3) ?
The integral from 1 to 6 of xsqrt(x+3) is 232/5