What is the integral of (1+x/3)^2 ?

The integral of (1+x/3)^2 is x+(x^2)/3+(x^3)/(27)+C

Popular >

integral of (1+x/3)^2

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

x + \frac{x ^{2}}{3} + \frac{x ^{3}}{27} + C

Solution steps

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

Expand

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

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

\int 1 d x = x

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

\int \frac{x ^{2}}{9} d x = \frac{x ^{3}}{27}

= x + \frac{x ^{2}}{3} + \frac{x ^{3}}{27}

Add a constant to the solution

= x + \frac{x ^{2}}{3} + \frac{x ^{3}}{27} + C

\int u^{2} - a^{2} d u

\int \frac{1}{( 1 - 0.04 x ) ^{0.3}} d x

\int sin (4 x) + cos (3 x) d x

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

\int \frac{x}{( 4 x ^{2} - 5 ) ^{6}} d x

What is the integral of (1+x/3)^2 ?
The integral of (1+x/3)^2 is x+(x^2)/3+(x^3)/(27)+C