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

f (x) = \frac{x ^{2}}{x + 2}, at x = 3

\int (6 x^{6} - 2)^{2} (36 x) d x

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

\frac{d y}{d x} = \frac{2 x - 1}{y ^{2}}

\frac{\partial}{\partial x} (x y (1 - 7 x - 6 y))

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