What is the integral of (5/(t^2)+4t^2) ?

The integral of (5/(t^2)+4t^2) is -5/t+(4t^3)/3+C

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integral of (5/(t^2)+4t^2)

\int (\frac{5}{t ^{2}} + 4 t^{2}) d t

- \frac{5}{t} + \frac{4 t ^{3}}{3} + C

Solution steps

\int \frac{5}{t ^{2}} + 4 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{5}{t ^{2}} d t + \int 4 t^{2} d t

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

\int 4 t^{2} d t = \frac{4 t ^{3}}{3}

= - \frac{5}{t} + \frac{4 t ^{3}}{3}

Add a constant to the solution

= - \frac{5}{t} + \frac{4 t ^{3}}{3} + C

\int \frac{1}{5 - x ^{2}} d x

\frac{d}{d x} (20 x^{3} - 6 x^{2} + x)

\frac{1}{s ^{2} - 4 s + 4}

\frac{d}{d x} (\frac{2}{x y})

\int_{0}^{\frac{π}{4}} 2 sec (x) d x

What is the integral of (5/(t^2)+4t^2) ?
The integral of (5/(t^2)+4t^2) is -5/t+(4t^3)/3+C