What is the integral of (2x+4)^2+sqrt(2x+2) ?

The integral of (2x+4)^2+sqrt(2x+2) is (4x^3)/3+8x^2+16x+1/3 (2x+2)^{3/2}+C

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integral of (2x+4)^2+sqrt(2x+2)

\int (2 x + 4)^{2} + 2 x + 2 d x

\frac{4 x ^{3}}{3} + 8 x^{2} + 16 x + \frac{1}{3} (2 x + 2)^{\frac{3}{2}} + C

Solution steps

\int (2 x + 4)^{2} + 2 x + 2 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 (2 x + 4)^{2} d x + \int 2 x + 2 d x

\int (2 x + 4)^{2} d x = \frac{4 x ^{3}}{3} + 8 x^{2} + 16 x

\int 2 x + 2 d x = \frac{1}{3} (2 x + 2)^{\frac{3}{2}}

= \frac{4 x ^{3}}{3} + 8 x^{2} + 16 x + \frac{1}{3} (2 x + 2)^{\frac{3}{2}}

Add a constant to the solution

= \frac{4 x ^{3}}{3} + 8 x^{2} + 16 x + \frac{1}{3} (2 x + 2)^{\frac{3}{2}} + C

t \to 0 lim (\frac{4}{t} - \frac{4}{t ^{2} + t})

\int \frac{cos ^{5} ( t )}{sin ( t )} d t

\frac{d}{d x} (10 + 3 x)

\frac{d}{d x} (y^{2} - x sin (y) - x y e^{- y})

\int (1 + x^{2}) d x

What is the integral of (2x+4)^2+sqrt(2x+2) ?
The integral of (2x+4)^2+sqrt(2x+2) is (4x^3)/3+8x^2+16x+1/3 (2x+2)^{3/2}+C