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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int_{1}^{\infty} \frac{1}{x ^{9}} d x

\frac{d N}{d t} = N (1 - 0.0008 N)

\frac{d}{d x} (7 x (x^{3} - 3 x + 2))

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

y = e^{- x}, y = 0, x = 0, x = ln (5)

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