What is the integral of 15/2 sqrt(t)+8e^{-t} ?

The integral of 15/2 sqrt(t)+8e^{-t} is 5t^{3/2}-8e^{-t}+C

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integral of 15/2 sqrt(t)+8e^{-t}

\int \frac{15}{2} t + 8 e^{- t} d t

5 t^{\frac{3}{2}} - 8 e^{- t} + C

Solution steps

\int \frac{15}{2} t + 8 e^{- t} 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{15}{2} t d t + \int 8 e^{- t} d t

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

\int 8 e^{- t} d t = - 8 e^{- t}

= 5 t^{\frac{3}{2}} - 8 e^{- t}

Add a constant to the solution

= 5 t^{\frac{3}{2}} - 8 e^{- t} + C

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\int_{0}^{t} t^{2} e^{- \frac{t}{3}} d t

What is the integral of 15/2 sqrt(t)+8e^{-t} ?
The integral of 15/2 sqrt(t)+8e^{-t} is 5t^{3/2}-8e^{-t}+C