What is the integral of (2sin(x)-sec^2(x)) ?

The integral of (2sin(x)-sec^2(x)) is -2cos(x)-tan(x)+C

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integral of (2sin(x)-sec^2(x))

\int (2 sin (x) - sec^{2} (x)) d x

- 2 cos (x) - tan (x) + C

Solution steps

\int 2 sin (x) - sec^{2} (x) 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 sec^{2} (x) d x

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

\int sec^{2} (x) d x = tan (x)

= - 2 cos (x) - tan (x)

Add a constant to the solution

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

4 e^{10 x}

y = 2 e^{- 2 x}

\int \frac{1}{w ^{5}} d w

(y^{2} + 9) d x - \frac{1}{( 2 x - 5 ) ^{2}} d y = 0

\frac{d}{d x} (11)

What is the integral of (2sin(x)-sec^2(x)) ?
The integral of (2sin(x)-sec^2(x)) is -2cos(x)-tan(x)+C