What is the integral of (2x+7)^2 ?

The integral of (2x+7)^2 is (4x^3)/3+14x^2+49x+C

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integral of (2x+7)^2

\int (2 x + 7)^{2} d x

\frac{4 x ^{3}}{3} + 14 x^{2} + 49 x + C

Solution steps

\int (2 x + 7)^{2} d x

Expand

(2 x + 7)^{2} : 4 x^{2} + 28 x + 49

= \int 4 x^{2} + 28 x + 49 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 4 x^{2} d x + \int 28 x d x + \int 49 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 28 x d x = 14 x^{2}

\int 49 d x = 49 x

= \frac{4 x ^{3}}{3} + 14 x^{2} + 49 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + 14 x^{2} + 49 x + C

\int \frac{1}{1 - sin ( 2 x )} d x

(1 - 2 t)^{- 4} (t^{2} - t)^{2}

\frac{\partial}{\partial y} (2 x^{\frac{y}{z}})

\int \frac{( 1 - x ) ^{2}}{x ^{2}} d x

\frac{d}{d x} (\frac{1}{2} ln^{2} (x))

What is the integral of (2x+7)^2 ?
The integral of (2x+7)^2 is (4x^3)/3+14x^2+49x+C