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

20 t^{2}

x \to 17 lim (x^{2} - 3 x + 1)

\frac{1}{3} (x^{2} + 2)^{\frac{3}{2}}

\int \frac{256}{x ^{3} - 16 x ^{2}} d x

\frac{d}{d x} (4 x + 7)

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