What is the integral of (7/(t^2)-5t^5) ?

The integral of (7/(t^2)-5t^5) is -7/t-(5t^6)/6+C

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integral of (7/(t^2)-5t^5)

\int (\frac{7}{t ^{2}} - 5 t^{5}) d t

- \frac{7}{t} - \frac{5 t ^{6}}{6} + C

Solution steps

\int \frac{7}{t ^{2}} - 5 t^{5} 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{7}{t ^{2}} d t - \int 5 t^{5} d t

\int \frac{7}{t ^{2}} d t = - \frac{7}{t}

\int 5 t^{5} d t = \frac{5 t ^{6}}{6}

= - \frac{7}{t} - \frac{5 t ^{6}}{6}

Add a constant to the solution

= - \frac{7}{t} - \frac{5 t ^{6}}{6} + C

\frac{\partial}{\partial x} (e^{x} + e^{y})

\int (\frac{3}{x ^{4}}) d x

\frac{\partial}{\partial y} (e^{y x})

\frac{\partial}{\partial x} (4 x + 9 y - 360)

\frac{d ^{2}}{d x ^{2}} (\frac{x}{x + 1})

What is the integral of (7/(t^2)-5t^5) ?
The integral of (7/(t^2)-5t^5) is -7/t-(5t^6)/6+C