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

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

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integral of (8^x-sec^2(x))

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

\frac{8 ^{x}}{3 ln ( 2 )} - tan (x) + C

Solution steps

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

\int 8^{x} d x = \frac{8 ^{x}}{3 ln ( 2 )}

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

= \frac{8 ^{x}}{3 ln ( 2 )} - tan (x)

Add a constant to the solution

= \frac{8 ^{x}}{3 ln ( 2 )} - tan (x) + C

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\frac{\partial}{\partial x} (\frac{- y + y ^{2} + 4 x ^{2}}{2})

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