What is the integral of sin(x)-4cos(x)+1 ?

The integral of sin(x)-4cos(x)+1 is -cos(x)-4sin(x)+x+C

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integral of sin(x)-4cos(x)+1

\int sin (x) - 4 cos (x) + 1 d x

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

Solution steps

\int sin (x) - 4 cos (x) + 1 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 sin (x) d x - \int 4 cos (x) d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\int g \cdot \frac{m}{k} (1 - e^{- \frac{k}{m} \cdot t}) d t

x \to \frac{5 π}{3} lim (cos (x))

f (x) = x^{3} - x^{2}, at x = - 1

\int x^{2} cos (x^{3} + 1) d x

\int (- \frac{4000}{x ^{2}}) d x

What is the integral of sin(x)-4cos(x)+1 ?
The integral of sin(x)-4cos(x)+1 is -cos(x)-4sin(x)+x+C