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

y^{^{'''}} - 3 y^{^{''}} + 2 y = 0

\int_{0}^{π} 3 cos^{2} (x) sin (x) d x

x \to 2 lim (8 - x)

\int 4^{x} sin (4^{x}) d x

x \to 0 + lim (sin (x) ln (4 x))

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