What is the integral of (-2sec(x)tan(x)-3sec^2(x)) ?

The integral of (-2sec(x)tan(x)-3sec^2(x)) is -2sec(x)-3tan(x)+C

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integral of (-2sec(x)tan(x)-3sec^2(x))

\int (- 2 sec (x) tan (x) - 3 sec^{2} (x)) d x

- 2 sec (x) - 3 tan (x) + C

Solution steps

\int - 2 sec (x) tan (x) - 3 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 sec (x) tan (x) d x - \int 3 sec^{2} (x) d x

\int 2 sec (x) tan (x) d x = 2 sec (x)

\int 3 sec^{2} (x) d x = 3 tan (x)

= - 2 sec (x) - 3 tan (x)

Add a constant to the solution

= - 2 sec (x) - 3 tan (x) + C

5 t \cdot \frac{d y}{d t} + 3 y = t

\frac{d x}{d t} = \frac{( 2 t ^{2} + x ^{2} )}{t x}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x} sin (x)

\int_{0}^{\infty} 1 d x

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

What is the integral of (-2sec(x)tan(x)-3sec^2(x)) ?
The integral of (-2sec(x)tan(x)-3sec^2(x)) is -2sec(x)-3tan(x)+C