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Popular >

integral of (4x+8)^2

Solution

\int (4 x + 8)^{2} d x

Solution

\frac{16 x ^{3}}{3} + 32 x^{2} + 64 x + C

Solution steps

\int (4 x + 8)^{2} d x

Expand

(4 x + 8)^{2} : 16 x^{2} + 64 x + 64

= \int 16 x^{2} + 64 x + 64 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 16 x^{2} d x + \int 64 x d x + \int 64 d x

\int 16 x^{2} d x = \frac{16 x ^{3}}{3}

\int 64 x d x = 32 x^{2}

\int 64 d x = 64 x

= \frac{16 x ^{3}}{3} + 32 x^{2} + 64 x

Add a constant to the solution

= \frac{16 x ^{3}}{3} + 32 x^{2} + 64 x + C

Popular Examples

integral of 5/(x^2+3)

\int \frac{5}{x ^{2} + 3} d x

integral of 1/(sqrt(1+4x-x^2))

\int \frac{1}{1 + 4 x - x ^{2}} d x

integral of sec(1/2)y

\int sec (\frac{1}{2}) y d y

integral of sqrt((1-x^2)^3)

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

integral of (x^3)/((x+1))

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

Frequently Asked Questions (FAQ)

What is the integral of (4x+8)^2 ?
The integral of (4x+8)^2 is (16x^3)/3+32x^2+64x+C