What is the integral of (2sqrt(t)-t-9/(t^2)) ?

The integral of (2sqrt(t)-t-9/(t^2)) is 4/3 t^{3/2}-(t^2)/2+9/t+C

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integral of (2sqrt(t)-t-9/(t^2))

\int (2 t - t - \frac{9}{t ^{2}}) d t

\frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} + \frac{9}{t} + C

Solution steps

\int 2 t - t - \frac{9}{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 2 t d t - \int t d t - \int \frac{9}{t ^{2}} d t

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

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

\int \frac{9}{t ^{2}} d t = - \frac{9}{t}

= \frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} - (- \frac{9}{t})

Simplify

= \frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} + \frac{9}{t}

Add a constant to the solution

= \frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} + \frac{9}{t} + C

x \to - 6 + lim (f (x))

\frac{\partial}{\partial x} (x^{4} + 6 y - 10)

f (x) = \frac{ln ( 8 x )}{e ^{5 x}}

x \to \frac{π}{2} lim (cot (2 x))

\frac{d}{d x} (3 sec (x) - 6 cos (x))

What is the integral of (2sqrt(t)-t-9/(t^2)) ?
The integral of (2sqrt(t)-t-9/(t^2)) is 4/3 t^{3/2}-(t^2)/2+9/t+C