What is the integral of 1/(2cos(x)) ?

The integral of 1/(2cos(x)) is 1/2 ln|tan(x)+sec(x)|+C

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integral of 1/(2cos(x))

\int \frac{1}{2 cos ( x )} d x

\frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int \frac{1}{2 cos ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{cos ( x )} d x

Rewrite using trig identities

= \frac{1}{2} \cdot \int sec (x) d x

Use the common integral:

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

= \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

\frac{110}{x ^{12}}

x^{^{''}} = - 9 x

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

\frac{1}{x}, 4

\int e^{8 x - 9} d x

What is the integral of 1/(2cos(x)) ?
The integral of 1/(2cos(x)) is 1/2 ln|tan(x)+sec(x)|+C