What is the integral of (2+y^2)^2 ?

The integral of (2+y^2)^2 is 4y+(4y^3)/3+(y^5)/5+C

Popular >

integral of (2+y^2)^2

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

4 y + \frac{4 y ^{3}}{3} + \frac{y ^{5}}{5} + C

Solution steps

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

Expand

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

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

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 y + \int 4 y^{2} d y + \int y^{4} d y

\int 4 d y = 4 y

\int 4 y^{2} d y = \frac{4 y ^{3}}{3}

\int y^{4} d y = \frac{y ^{5}}{5}

= 4 y + \frac{4 y ^{3}}{3} + \frac{y ^{5}}{5}

Add a constant to the solution

= 4 y + \frac{4 y ^{3}}{3} + \frac{y ^{5}}{5} + C

\frac{( 6 x ^{9} + x ^{8} )}{2 x ^{4}}

\frac{\partial}{\partial x} (y + 2 x)

\int_{1}^{3} 3 x^{- \frac{3}{2}} d x

\int (5 x^{4} + 12 x^{3} + 6 x - 2) d x

(2 y + 2 t - 3) d t + (8 y + 2 t - 1) d y = 0

What is the integral of (2+y^2)^2 ?
The integral of (2+y^2)^2 is 4y+(4y^3)/3+(y^5)/5+C