What is the integral of 2e^t+3sin(t) ?

The integral of 2e^t+3sin(t) is 2e^t-3cos(t)+C

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integral of 2e^t+3sin(t)

\int 2 e^{t} + 3 sin (t) d t

2 e^{t} - 3 cos (t) + C

Solution steps

\int 2 e^{t} + 3 sin (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 2 e^{t} d t + \int 3 sin (t) d t

\int 2 e^{t} d t = 2 e^{t}

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

= 2 e^{t} - 3 cos (t)

Add a constant to the solution

= 2 e^{t} - 3 cos (t) + C

\int x \cdot 1 + x d x

\int x 2 x^{2} - 3 d x

\int t cos^{2} (2 t) d t

\int e^{- x} (2 e^{- x} + 3)^{9} d x

\int \frac{2 x ^{2}}{x ^{3} x ^{6} - 9} d x

What is the integral of 2e^t+3sin(t) ?
The integral of 2e^t+3sin(t) is 2e^t-3cos(t)+C