What is the integral of 2/3 t^{3/2}-8sin(t)+C ?

The integral of 2/3 t^{3/2}-8sin(t)+C is 4/15 t^{5/2}+8cos(t)+Ct+C

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integral of 2/3 t^{3/2}-8sin(t)+C

\int \frac{2}{3} t^{\frac{3}{2}} - 8 sin (t) + C d t

\frac{4}{15} t^{\frac{5}{2}} + 8 cos (t) + Ct + C

Solution steps

\int \frac{2}{3} t^{\frac{3}{2}} - 8 sin (t) + C 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{2}{3} t^{\frac{3}{2}} d t - \int 8 sin (t) d t + \int C d t

\int \frac{2}{3} t^{\frac{3}{2}} d t = \frac{4}{15} t^{\frac{5}{2}}

\int 8 sin (t) d t = - 8 cos (t)

\int C d t = Ct

= \frac{4}{15} t^{\frac{5}{2}} - (- 8 cos (t)) + Ct

Simplify

= \frac{4}{15} t^{\frac{5}{2}} + 8 cos (t) + Ct

Add a constant to the solution

= \frac{4}{15} t^{\frac{5}{2}} + 8 cos (t) + Ct + C

\frac{\partial}{\partial x} (e^{x^{2} + y} - 2 x y)

y^{^{'}} = x y (y + 2)

n = 1 \sum \infty \frac{9}{n ^{3}}

n = 0 \sum \infty 4 (\frac{3}{4})^{n}

\frac{d}{d x} (\frac{ln ( x + 2 )}{4 x ^{- 2}})

What is the integral of 2/3 t^{3/2}-8sin(t)+C ?
The integral of 2/3 t^{3/2}-8sin(t)+C is 4/15 t^{5/2}+8cos(t)+Ct+C