What is the integral of 5t^2+e^{0.39t}+2 ?

The integral of 5t^2+e^{0.39t}+2 is 1.66666…t^3+2.56410…e^{0.39t}+2t+C

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integral of 5t^2+e^{0.39t}+2

\int 5 t^{2} + e^{0.39 t} + 2 d t

1.66666 \dots t^{3} + 2.56410 \dots e^{0.39 t} + 2 t + C

Solution steps

\int 5 t^{2} + e^{0.39 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 5 t^{2} d t + \int e^{0.39 t} d t + \int 2 d t

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

\int e^{0.39 t} d t = 2.56410 \dots e^{0.39 t}

\int 2 d t = 2 t

= \frac{5 t ^{3}}{3} + 2.56410 \dots e^{0.39 t} + 2 t

Simplify

= 1.66666 \dots t^{3} + 2.56410 \dots e^{0.39 t} + 2 t

Add a constant to the solution

= 1.66666 \dots t^{3} + 2.56410 \dots e^{0.39 t} + 2 t + C

\int \frac{t}{a + b t ^{2}} d t

\int 9 e^{- 9 x} d x

sin^{2} (x), sin^{3} (x)

\frac{d}{d x} (sin (\frac{1}{x}) x^{3})

g (x) = ln (x^{2}), (e, 2)

What is the integral of 5t^2+e^{0.39t}+2 ?
The integral of 5t^2+e^{0.39t}+2 is 1.66666…t^3+2.56410…e^{0.39t}+2t+C