What is the integral of 2sin(x)+1 ?

The integral of 2sin(x)+1 is -2cos(x)+x+C

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integral of 2sin(x)+1

\int 2 sin (x) + 1 d x

- 2 cos (x) + x + C

Solution steps

\int 2 sin (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 2 sin (x) d x + \int 1 d x

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

\int 1 d x = x

= - 2 cos (x) + x

Add a constant to the solution

= - 2 cos (x) + x + C

\int_{0}^{\frac{π}{3}} (sec^{2} (x)) d x

y = sin (x cos (x))

\frac{d}{d x} (x (x - 1)^{2})

\frac{\partial}{\partial x} (\frac{4 x}{5 + y})

\frac{1}{c + k e ^{c}}