What is the integral of 1/(cos(x)) ?

The integral of 1/(cos(x)) is ln|tan(x)+sec(x)|+C

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integral of 1/(cos(x))

\int \frac{1}{cos ( x )} d x

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{1}{cos ( x )} d x

Rewrite using trig identities

= \int sec (x) d x

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ + C

\int_{1}^{3} \frac{x ^{2} + 1}{4 x - x ^{2}} d x

x y^{^{'}} - y = 3 x ln (x)

\frac{1}{10} x^{5} - 3 x^{3}

\int \frac{3 x - 11}{x ^{3} - 5 x ^{2}} d x

\int - 8 y^{3} d y

What is the integral of 1/(cos(x)) ?
The integral of 1/(cos(x)) is ln|tan(x)+sec(x)|+C