What is the integral of sqrt(t)+1/(t^3)+7/(t^2) ?

The integral of sqrt(t)+1/(t^3)+7/(t^2) is 2/3 t^{3/2}-1/(2t^2)-7/t+C

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integral of sqrt(t)+1/(t^3)+7/(t^2)

\int t + \frac{1}{t ^{3}} + \frac{7}{t ^{2}} d t

\frac{2}{3} t^{\frac{3}{2}} - \frac{1}{2 t ^{2}} - \frac{7}{t} + C

Solution steps

\int t + \frac{1}{t ^{3}} + \frac{7}{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 t d t + \int \frac{1}{t ^{3}} d t + \int \frac{7}{t ^{2}} d t

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

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

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

= \frac{2}{3} t^{\frac{3}{2}} - \frac{1}{2 t ^{2}} - \frac{7}{t}

Add a constant to the solution

= \frac{2}{3} t^{\frac{3}{2}} - \frac{1}{2 t ^{2}} - \frac{7}{t} + C

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What is the integral of sqrt(t)+1/(t^3)+7/(t^2) ?
The integral of sqrt(t)+1/(t^3)+7/(t^2) is 2/3 t^{3/2}-1/(2t^2)-7/t+C