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Popular >

integral of (2+x)^2

Solution

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

Solution

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

Solution steps

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

Expand

(2 + x)^{2} : 4 + 4 x + x^{2}

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

\int 4 d x = 4 x

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

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

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

Add a constant to the solution

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

Popular Examples

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

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\int sec (10 x) tan (10 x) d x

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

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

integral of (1/(\sqrt[5]{x)}+5/(e^{3x)})

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

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

Frequently Asked Questions (FAQ)

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