What is the integral of (e 1/t+2)/(t^2) ?

The integral of (e 1/t+2)/(t^2) is -e/(2t^2)-2/t+C

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integral of (e 1/t+2)/(t^2)

\int \frac{e \frac{1}{t} + 2}{t ^{2}} d t

- \frac{e}{2 t ^{2}} - \frac{2}{t} + C

Solution steps

\int \frac{e \frac{1}{t} + 2}{t ^{2}} d t

Expand

\frac{e \frac{1}{t} + 2}{t ^{2}} : \frac{e}{t ^{3}} + \frac{2}{t ^{2}}

= \int \frac{e}{t ^{3}} + \frac{2}{t ^{2}} d t

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{e}{t ^{3}} d t + \int \frac{2}{t ^{2}} d t

\int \frac{e}{t ^{3}} d t = - \frac{e}{2 t ^{2}}

\int \frac{2}{t ^{2}} d t = - \frac{2}{t}

= - \frac{e}{2 t ^{2}} - \frac{2}{t}

Add a constant to the solution

= - \frac{e}{2 t ^{2}} - \frac{2}{t} + C

x \to 6 lim (\frac{x}{x ^{2} + 1})

x \to 1 - lim (\frac{1 + x}{1 - x})

f (x) = \frac{x}{1 - ln ( x - 1 )}

\int y 9 - y d y

x \to 3 - lim (\frac{5}{x ^{2} - 9})

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