What is the integral of 3sec(2)(x)+2x-8x ?

The integral of 3sec(2)(x)+2x-8x is 3/2 sec(2)x^2-3x^2+C

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integral of 3sec(2)(x)+2x-8x

\int 3 sec (2) (x) + 2 x - 8 x d x

\frac{3}{2} sec (2) x^{2} - 3 x^{2} + C

Solution steps

\int 3 sec (2) x + 2 x - 8 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 3 sec (2) x d x + \int 2 x d x - \int 8 x d x

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

\int 2 x d x = x^{2}

\int 8 x d x = 4 x^{2}

= \frac{3}{2} sec (2) x^{2} + x^{2} - 4 x^{2}

Simplify

= \frac{3}{2} sec (2) x^{2} - 3 x^{2}

Add a constant to the solution

= \frac{3}{2} sec (2) x^{2} - 3 x^{2} + C

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What is the integral of 3sec(2)(x)+2x-8x ?
The integral of 3sec(2)(x)+2x-8x is 3/2 sec(2)x^2-3x^2+C