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Popular >

integral of (a+x)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of e^{tan(20x)}sec^2(20x)

\int e^{t a n (20 x)} sec^{2} (20 x) d x

integral of arctan(x)*x

\int arctan (x) \cdot x d x

integral of 3/((1+9x^2)^{3/2)}

\int \frac{3}{( 1 + 9 x ^{2} ) ^{\frac{3}{2}}} d x

integral of x/(5+x^2)

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

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

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

Frequently Asked Questions (FAQ)

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