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

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

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

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

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

Solution steps

\int \frac{2}{3} t^{\frac{3}{2}} - 2 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 2 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 2 sin (t) d t = - 2 cos (t)

\int C d t = Ct

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

Simplify

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

Add a constant to the solution

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

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7 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

f^{'} (t)

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