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

The integral from 1 to 3 of 3xsqrt(2x+3) is 162/5

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

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

\frac{162}{5}

Decimal Notation

32.4

Solution steps

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

Take the constant out:

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

= 3 \cdot \int_{1}^{3} x 2 x + 3 d x

Apply u-substitution

: \int_{5}^{9} \frac{u ( u - 3 )}{4} d u

= 3 \cdot \int_{5}^{9} \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

= 3 \cdot \frac{1}{4} \cdot \int_{5}^{9} u (u - 3) d u

Expand

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

= 3 \cdot \frac{1}{4} \cdot \int_{5}^{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

= 3 \cdot \frac{1}{4} (\int_{5}^{9} u^{\frac{3}{2}} d u - \int_{5}^{9} 3 u d u)

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

\int_{5}^{9} 3 u d u = 54 - 105

= 3 \cdot \frac{1}{4} (\frac{486}{5} - 105 - (54 - 105))

Simplify

3 \cdot \frac{1}{4} (\frac{486}{5} - 105 - (54 - 105)) : \frac{162}{5}

= \frac{162}{5}

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What is the integral from 1 to 3 of 3xsqrt(2x+3) ?
The integral from 1 to 3 of 3xsqrt(2x+3) is 162/5