What is the integral of 7^x-sec^2(x) ?

The integral of 7^x-sec^2(x) is (7^x)/(ln(7))-tan(x)+C

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integral of 7^x-sec^2(x)

\int 7^{x} - sec^{2} (x) d x

\frac{7 ^{x}}{ln ( 7 )} - tan (x) + C

Solution steps

\int 7^{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 7^{x} d x - \int sec^{2} (x) d x

\int 7^{x} d x = \frac{7 ^{x}}{ln ( 7 )}

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

= \frac{7 ^{x}}{ln ( 7 )} - tan (x)

Add a constant to the solution

= \frac{7 ^{x}}{ln ( 7 )} - tan (x) + C

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\frac{d}{d x} (\frac{x ^{2} - 6 x - 1}{( x - 3 ) ^{2}})

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = 1

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What is the integral of 7^x-sec^2(x) ?
The integral of 7^x-sec^2(x) is (7^x)/(ln(7))-tan(x)+C