What is the integral of (5cos(x)-3sin(x)) ?

The integral of (5cos(x)-3sin(x)) is 5sin(x)+3cos(x)+C

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integral of (5cos(x)-3sin(x))

\int (5 cos (x) - 3 sin (x)) d x

5 sin (x) + 3 cos (x) + C

Solution steps

\int 5 cos (x) - 3 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 5 cos (x) d x - \int 3 sin (x) d x

\int 5 cos (x) d x = 5 sin (x)

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

= 5 sin (x) - (- 3 cos (x))

Simplify

= 5 sin (x) + 3 cos (x)

Add a constant to the solution

= 5 sin (x) + 3 cos (x) + C

\int x^{2} (2 x^{3} + 5)^{4} d x

\int cos (6 x) d x

\int (x^{5} + 1) e^{x^{6} + 6 x} d x

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

n = 1 \sum \infty \frac{4}{n ^{2} + 5 n + 6}

What is the integral of (5cos(x)-3sin(x)) ?
The integral of (5cos(x)-3sin(x)) is 5sin(x)+3cos(x)+C