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

The integral of 4/15 t^{5/2}+3cos(t)+Ct+C is 8/105 t^{7/2}+3sin(t)+(Ct^2)/2+Ct+C

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

\int \frac{4}{15} t^{\frac{5}{2}} + 3 cos (t) + Ct + C d t

\frac{8}{105} t^{\frac{7}{2}} + 3 sin (t) + \frac{C t ^{2}}{2} + Ct + C

Solution steps

\int \frac{4}{15} t^{\frac{5}{2}} + 3 cos (t) + Ct + 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{4}{15} t^{\frac{5}{2}} d t + \int 3 cos (t) d t + \int Ct d t + \int C d t

\int \frac{4}{15} t^{\frac{5}{2}} d t = \frac{8}{105} t^{\frac{7}{2}}

\int 3 cos (t) d t = 3 sin (t)

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

\int C d t = Ct

= \frac{8}{105} t^{\frac{7}{2}} + 3 sin (t) + \frac{C t ^{2}}{2} + Ct

Add a constant to the solution

= \frac{8}{105} t^{\frac{7}{2}} + 3 sin (t) + \frac{C t ^{2}}{2} + Ct + C

What is the integral of 4/15 t^{5/2}+3cos(t)+Ct+C ?
The integral of 4/15 t^{5/2}+3cos(t)+Ct+C is 8/105 t^{7/2}+3sin(t)+(Ct^2)/2+Ct+C