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

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

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integral of 3cos(t)-2sin(t)

\int 3 cos (t) - 2 sin (t) d t

3 sin (t) + 2 cos (t) + C

Solution steps

\int 3 cos (t) - 2 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 3 cos (t) d t - \int 2 sin (t) d t

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

\int 2 sin (t) d t = - 2 cos (t)

= 3 sin (t) - (- 2 cos (t))

Simplify

= 3 sin (t) + 2 cos (t)

Add a constant to the solution

= 3 sin (t) + 2 cos (t) + C

e^{4 t} (t^{2} + 3 t + 5)

\int (- 9 x^{2} sec (3 x^{3} + 1)) d x

\frac{d}{d x} ((4 x)^{5 x})

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

x \to 1 lim (1 - 2 - x)

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