What is the integral of 2e^t-3cos(t) ?

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

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integral of 2e^t-3cos(t)

\int 2 e^{t} - 3 cos (t) d t

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

Solution steps

\int 2 e^{t} - 3 cos (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 cos (t) d t

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

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

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

Add a constant to the solution

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

\int x (3 x^{2} + 1)^{4} d x

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\int - \frac{cos ( 4 x )}{4} d x

\int \frac{2}{3 - 5 x} d x

\int 16 x^{2} 3 7 - 4 x^{3} d x

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