What is the integral of 2cos(2x)-1 ?

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

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integral of 2cos(2x)-1

\int 2 cos (2 x) - 1 d x

sin (2 x) - x + C

Solution steps

\int 2 cos (2 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 cos (2 x) d x - \int 1 d x

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

\int 1 d x = x

= sin (2 x) - x

Add a constant to the solution

= sin (2 x) - x + C

cos^{2} (2 t)

\frac{( ( s + 1 ) ^{2} + 1 )}{s}

\int 2 x (x^{2} + 3)^{7} d x

x - e^{3 x}