What is the integral of (5cos(x)-4sin(x)) ?

The integral of (5cos(x)-4sin(x)) is 5sin(x)+4cos(x)+C

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integral of (5cos(x)-4sin(x))

\int (5 cos (x) - 4 sin (x)) d x

5 sin (x) + 4 cos (x) + C

Solution steps

\int 5 cos (x) - 4 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 4 sin (x) d x

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

\int 4 sin (x) d x = - 4 cos (x)

= 5 sin (x) - (- 4 cos (x))

Simplify

= 5 sin (x) + 4 cos (x)

Add a constant to the solution

= 5 sin (x) + 4 cos (x) + C

\frac{1}{x - 2}

f (x) = e^{4 x}

\frac{d ^{2}}{d x ^{2}} (x^{\frac{8}{9}} + 5 x)

\int_{3}^{\infty} \frac{1}{x} d x

\int_{0}^{4} (x^{2} - 4 x) d x

What is the integral of (5cos(x)-4sin(x)) ?
The integral of (5cos(x)-4sin(x)) is 5sin(x)+4cos(x)+C