What is the integral of 1/(sec(θ)) ?

The integral of 1/(sec(θ)) is sin(θ)+C

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integral of 1/(sec(θ))

\int \frac{1}{sec ( θ )} d θ

sin (θ) + C

Solution steps

\int \frac{1}{sec ( θ )} d θ

Rewrite using trig identities

= \int cos (θ) d θ

Use the common integral:

\int cos (θ) d θ = sin (θ)

= sin (θ)

Add a constant to the solution

= sin (θ) + C

x + x (y^{^{'}}) 2 - 1 = 0

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

\frac{d}{d x} (y - 3 x)

\frac{d}{d x} (2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5)

2 x y^{^{'}} + y = 6 x, y (4) = 20