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Popular >

integral of (x+8)^2

Solution

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

Solution

\frac{x ^{3}}{3} + 8 x^{2} + 64 x + C

Solution steps

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

Expand

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

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

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

\int 16 x d x = 8 x^{2}

\int 64 d x = 64 x

= \frac{x ^{3}}{3} + 8 x^{2} + 64 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 8 x^{2} + 64 x + C

Popular Examples

integral from-2 to 3 of (10)/(x^4)

\int_{- 2}^{3} \frac{10}{x ^{4}} d x

integral of e^{x^2-5x}

\int e^{x^{2} - 5 x} d x

limit as x approaches 0-of 1/(e^x)

x \to 0 - lim (\frac{1}{e ^{x}})

integral of 1/(-x+1)

\int \frac{1}{- x + 1} d x

derivative of (x^2+4/(2x))

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

Frequently Asked Questions (FAQ)

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