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

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

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integral of 2xy-sec^2(x)

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

- tan (x) + y x^{2} + C

Solution steps

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

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

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

= - tan (x) + y x^{2}

Add a constant to the solution

= - tan (x) + y x^{2} + C

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