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

The integral from-1 to 3 of (2x+3)^2 is 364/3

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

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

\frac{364}{3}

Decimal

121.33333 \dots

Solution steps

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

Expand

(2 x + 3)^{2} : 4 x^{2} + 12 x + 9

= \int_{- 1}^{3} 4 x^{2} + 12 x + 9 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{3} 4 x^{2} d x + \int_{- 1}^{3} 12 x d x + \int_{- 1}^{3} 9 d x

\int_{- 1}^{3} 4 x^{2} d x = \frac{112}{3}

\int_{- 1}^{3} 12 x d x = 48

\int_{- 1}^{3} 9 d x = 36

= \frac{112}{3} + 48 + 36

Simplify

\frac{112}{3} + 48 + 36 : \frac{364}{3}

= \frac{364}{3}

\frac{x - y}{x}

\frac{d}{d x} (\frac{x ^{2} ( x + 3 )}{16 ( x ^{2} - 4 )})

\frac{d y}{d x} = y, y (11) = 3

\int \frac{1}{x ^{2} - x - 6} d x

\frac{\partial}{\partial x} (- \frac{y}{x})

What is the integral from-1 to 3 of (2x+3)^2 ?
The integral from-1 to 3 of (2x+3)^2 is 364/3