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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int tan (x) sec^{4} (x) d x

y^{^{''}} + 2 y^{^{'}} + 3 y = 0

y = x^{3} - 3 x^{2} - 27 x + 14, y = x + 14

\int \frac{x ^{3} + 6 x ^{2} + 3 x + 6}{x ^{3} + 2 x ^{2}} d x

\int \frac{x ^{- 1} - x ^{- 2} + x ^{- 3}}{x ^{2}} d x

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