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

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

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

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

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

Solution steps

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

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

\int \frac{csc ^{2} ( x )}{cot ( x ) + 1} d x

f (x) = (2 + 5 x) (5 - 4 x), at x = 1

y^{^{'}} - y = 5.2

\int sin (3 z) cos (2) (3 z) d z

f (t) = t cos (2 t) e^{- t}, at t = 3

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