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

\frac{d}{d x} (sin^{5} (ln (e^{3 x - 1})))

\int t e^{- t} - 2 d t

\int 2 x + 6 cos (x) d x

\int (25 - x^{2})^{\frac{1}{2}} d x

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