What is the integral of (sec^2(x)+5) ?

The integral of (sec^2(x)+5) is tan(x)+5x+C

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integral of (sec^2(x)+5)

\int (sec^{2} (x) + 5) d x

tan (x) + 5 x + C

Solution steps

\int sec^{2} (x) + 5 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 5 d x

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

\int 5 d x = 5 x

= tan (x) + 5 x

Add a constant to the solution

= tan (x) + 5 x + C

\int (x^{2} + 1)^{5} \cdot x d x

\frac{d ^{3}}{d x ^{3}} (ln (x))

\frac{d}{d x} (\frac{6}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

y = x^{- 8 c o s (x)}

y = sin (t) + \frac{1}{6} e^{t}, (π, \frac{1}{6} e^{π})

What is the integral of (sec^2(x)+5) ?
The integral of (sec^2(x)+5) is tan(x)+5x+C