What is the integral of sec^2(θ)+7 ?

The integral of sec^2(θ)+7 is tan(θ)+7θ+C

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integral of sec^2(θ)+7

\int sec^{2} (θ) + 7 d θ

tan (θ) + 7 θ + C

Solution steps

\int sec^{2} (θ) + 7 d θ

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} (θ) d θ + \int 7 d θ

\int sec^{2} (θ) d θ = tan (θ)

\int 7 d θ = 7 θ

= tan (θ) + 7 θ

Add a constant to the solution

= tan (θ) + 7 θ + C

y = \frac{5}{6} x^{2}, y = \frac{11}{6} - x^{2}

\frac{d}{d x} (e^{r x} r)

f (x) = x^{2} - 5 x + 5, at x = 6

x^{2} cos (x), 0.1

f (x) = - 25 x^{2} + 150 x - 182