What is the integral from-1 to 2 of xsqrt(2x+3) ?

The integral from-1 to 2 of xsqrt(2x+3) is (7sqrt(7)+2)/5

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integral from-1 to 2 of xsqrt(2x+3)

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

\frac{7 7 + 2}{5}

Decimal Notation

4.10405 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{7} \frac{u ( u - 3 )}{4} d u

= \int_{1}^{7} \frac{u ( u - 3 )}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{1}^{7} u (u - 3) d u

Expand

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

= \frac{1}{4} \cdot \int_{1}^{7} 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

= \frac{1}{4} (\int_{1}^{7} u^{\frac{3}{2}} d u - \int_{1}^{7} 3 u d u)

\int_{1}^{7} u^{\frac{3}{2}} d u = \frac{98 7 - 2}{5}

\int_{1}^{7} 3 u d u = 147 - 2

= \frac{1}{4} (\frac{98 7 - 2}{5} - (147 - 2))

Simplify

\frac{1}{4} (\frac{98 7 - 2}{5} - (147 - 2)) : \frac{7 7 + 2}{5}

= \frac{7 7 + 2}{5}

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What is the integral from-1 to 2 of xsqrt(2x+3) ?
The integral from-1 to 2 of xsqrt(2x+3) is (7sqrt(7)+2)/5