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

The integral from-2 to 3 of (3x+2)(x+3) is 185/2

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

\int_{- 2}^{3} (3 x + 2) (x + 3) d x

\frac{185}{2}

Decimal

92.5

Solution steps

\int_{- 2}^{3} (3 x + 2) (x + 3) d x

Multiply by the conjugate of

3 x + 2 : \frac{9 x ^{2} - 4}{3 x - 2}

= \int_{- 2}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x

Find undefined (singularity) points:

x = \frac{2}{3}

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 2}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x + \int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x

\int_{- 2}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x = \frac{128}{27}

\int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x + 3) d x = \frac{4739}{54}

= \frac{128}{27} + \frac{4739}{54}

Simplify

\frac{128}{27} + \frac{4739}{54} : \frac{185}{2}

= \frac{185}{2}

What is the integral from-2 to 3 of (3x+2)(x+3) ?
The integral from-2 to 3 of (3x+2)(x+3) is 185/2