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

The integral of ((tsqrt(t)+sqrt(t)))/(t^2) is 2sqrt(t)-2/(sqrt(t))+C

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integral of ((tsqrt(t)+sqrt(t)))/(t^2)

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

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

Solution steps

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

\frac{t t + t}{t ^{2}} = (\frac{t t}{t ^{2}} + \frac{t}{t ^{2}})

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

Simplify

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

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

\int \frac{1}{t} d t = 2 t

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

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

Add a constant to the solution

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

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