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

The integral of ((y+1))/(y^3) is -1/y-1/(2y^2)+C

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integral of ((y+1))/(y^3)

integral

\frac{( y + 1 )}{y ^{3}}

- \frac{1}{y} - \frac{1}{2 y ^{2}} + C

Solution steps

\int \frac{y + 1}{y ^{3}} d y

Expand

\frac{y + 1}{y ^{3}} : \frac{1}{y ^{2}} + \frac{1}{y ^{3}}

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

\int \frac{1}{y ^{2}} d y = - \frac{1}{y}

\int \frac{1}{y ^{3}} d y = - \frac{1}{2 y ^{2}}

= - \frac{1}{y} - \frac{1}{2 y ^{2}}

Add a constant to the solution

= - \frac{1}{y} - \frac{1}{2 y ^{2}} + C

\frac{tan ( x )}{2}

\frac{ln ( t )}{( 1 + t ^{2} )}

t^{- 2}

e^{- 3 x}

(3 - x)^{3}

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