What is the integral of sec^2(x)+6 ?

The integral of sec^2(x)+6 is tan(x)+6x+C

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integral of sec^2(x)+6

\int sec^{2} (x) + 6 d x

tan (x) + 6 x + C

Solution steps

\int sec^{2} (x) + 6 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 6 d x

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

\int 6 d x = 6 x

= tan (x) + 6 x

Add a constant to the solution

= tan (x) + 6 x + C

\frac{( e ^{- 4 s} )}{( s + 2 ) ^{3}}

\frac{\partial}{\partial x} ((x - 3)^{2} + (y - 2)^{2})

{\frac{1}{s ^{4} - 9}}

- 5 t + 3 + t^{7}