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

The integral of ((2+sqrt(y))^2)/(sqrt(y)) is 8sqrt(y)+4y+2/3 y^{3/2}+C

Popular >

integral of ((2+sqrt(y))^2)/(sqrt(y))

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

8 y + 4 y + \frac{2}{3} y^{\frac{3}{2}} + C

Solution steps

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

Expand

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

= \int \frac{4}{y} + 4 + y 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 \frac{4}{y} d y + \int 4 d y + \int y d y

\int \frac{4}{y} d y = 8 y

\int 4 d y = 4 y

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

= 8 y + 4 y + \frac{2}{3} y^{\frac{3}{2}}

Add a constant to the solution

= 8 y + 4 y + \frac{2}{3} y^{\frac{3}{2}} + C

\int \frac{1}{sin ( x ) ( sin ( x ) + cos ( x ) )} d x

\int \frac{1}{e ^{x} x} d x

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

\int 6 x^{5} (1 - x^{6})^{2} d x

\int sin (\frac{x}{3}) cos (\frac{x}{3}) d x

What is the integral of ((2+sqrt(y))^2)/(sqrt(y)) ?
The integral of ((2+sqrt(y))^2)/(sqrt(y)) is 8sqrt(y)+4y+2/3 y^{3/2}+C