What is the integral of (-7sec(x)tan(x)+8sec^2(x)) ?

The integral of (-7sec(x)tan(x)+8sec^2(x)) is -7sec(x)+8tan(x)+C

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integral of (-7sec(x)tan(x)+8sec^2(x))

\int (- 7 sec (x) tan (x) + 8 sec^{2} (x)) d x

- 7 sec (x) + 8 tan (x) + C

Solution steps

\int - 7 sec (x) tan (x) + 8 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 7 sec (x) tan (x) d x + \int 8 sec^{2} (x) d x

\int 7 sec (x) tan (x) d x = 7 sec (x)

\int 8 sec^{2} (x) d x = 8 tan (x)

= - 7 sec (x) + 8 tan (x)

Add a constant to the solution

= - 7 sec (x) + 8 tan (x) + C

\frac{d}{d x} (a^{x})

d er i v a t i v e f (x) = 2 ln (2 x)

\frac{d y}{d x} + x^{- 1} y = x^{- 1} cos (x) y^{- 2}

\int_{1}^{\infty} (\frac{1}{x}) d x

x y^{^{'}} + 3 y = \frac{2 e ^{- 2 x}}{x ^{2}}

What is the integral of (-7sec(x)tan(x)+8sec^2(x)) ?
The integral of (-7sec(x)tan(x)+8sec^2(x)) is -7sec(x)+8tan(x)+C