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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{d y}{d x} = \frac{e ^{x}}{e ^{y}}

y^{^{''}} - 10 y^{^{'}} + 9 y = 0

y = x^{4} + 4 x^{2} - x, (1, 4)

y = \frac{1}{3} x^{3} - 3 x^{2} + 5 x

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