What is the integral from 1 to 4 of (y+2)/(y^2) ?

The integral from 1 to 4 of (y+2)/(y^2) is 2ln(2)+3/2

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integral from 1 to 4 of (y+2)/(y^2)

\int_{1}^{4} \frac{y + 2}{y ^{2}} d y

2 ln (2) + \frac{3}{2}

Solution steps

\int_{1}^{4} \frac{y + 2}{y ^{2}} d y

Expand

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

= \int_{1}^{4} \frac{1}{y} + \frac{2}{y ^{2}} 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_{1}^{4} \frac{1}{y} d y + \int_{1}^{4} \frac{2}{y ^{2}} d y

\int_{1}^{4} \frac{1}{y} d y = 2 ln (2)

\int_{1}^{4} \frac{2}{y ^{2}} d y = \frac{3}{2}

= 2 ln (2) + \frac{3}{2}

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What is the integral from 1 to 4 of (y+2)/(y^2) ?
The integral from 1 to 4 of (y+2)/(y^2) is 2ln(2)+3/2