What is the integral of (sqrt(t))/(t^3) ?

The integral of (sqrt(t))/(t^3) is -2/(3t^{3/2)}+C

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integral of (sqrt(t))/(t^3)

\int \frac{t}{t ^{3}} d t

- \frac{2}{3 t ^{\frac{3}{2}}} + C

Solution steps

\int \frac{t}{t ^{3}} d t

Simplify

\frac{t}{t ^{3}} : \frac{1}{t ^{\frac{5}{2}}}

= \int \frac{1}{t ^{\frac{5}{2}}} d t

Apply the Power Rule

: - \frac{2}{3 t ^{\frac{3}{2}}}

= - \frac{2}{3 t ^{\frac{3}{2}}}

Add a constant to the solution

= - \frac{2}{3 t ^{\frac{3}{2}}} + C

x \to 0 lim (\frac{x}{1 - cos ( x )})

\frac{d}{d x} ((2 cos (2 x) + sin (3 x) + 3)^{2})

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

\frac{d y}{d t} - 2 t y = - 9 t^{2} e^{t^{2}}

What is the integral of (sqrt(t))/(t^3) ?
The integral of (sqrt(t))/(t^3) is -2/(3t^{3/2)}+C