What is the integral of (3cos(x)+2sin(x)) ?

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

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integral of (3cos(x)+2sin(x))

\int (3 cos (x) + 2 sin (x)) d x

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

Solution steps

\int 3 cos (x) + 2 sin (x) d x

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 (x) d x + \int 2 sin (x) d x

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

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

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

Add a constant to the solution

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

\int \frac{4 x}{x - 5} d x

\int csc^{5} (π x) cot^{3} (π x) d x

\int (x + 5)^{\frac{3}{2}} d x

\int \frac{1}{x ^{3} ( x - 1 )} d x

\int \frac{x + 2}{( x ^{2} + 4 x + 6 ) ^{5}} d x

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