What is the integral of 5sin(x)-2cos(x) ?

The integral of 5sin(x)-2cos(x) is -5cos(x)-2sin(x)+C

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integral of 5sin(x)-2cos(x)

\int 5 sin (x) - 2 cos (x) d x

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

Solution steps

\int 5 sin (x) - 2 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 5 sin (x) d x - \int 2 cos (x) d x

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

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

= - 5 cos (x) - 2 sin (x)

Add a constant to the solution

= - 5 cos (x) - 2 sin (x) + C

\int_{0}^{4} 4 t^{2} + 9 t^{4} d t

x \to 5 lim (csc (\frac{π x}{4}))

\frac{\partial}{\partial x} (x \cdot sin (2 y))

\frac{d}{d y} (x^{2} - y)

\int \frac{x ^{2} + x + 3}{x - 2} d x

What is the integral of 5sin(x)-2cos(x) ?
The integral of 5sin(x)-2cos(x) is -5cos(x)-2sin(x)+C