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

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

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integral of 2sin(x)+5

\int 2 sin (x) + 5 d x

- 2 cos (x) + 5 x + C

Solution steps

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

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

\int 5 d x = 5 x

= - 2 cos (x) + 5 x

Add a constant to the solution

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

\frac{e ^{x}}{x - 1}

\int 3 cos (3 t) d t

x \to 2 lim (\frac{2 x - 3}{x + 1})

(3, 1), (- 2, - 2)

n = 0 \sum \infty (n x)^{n}