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

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

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integral of (cos(x))/(cos^2(x))

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

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

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

Simplify

\frac{cos ( x )}{cos ^{2} ( x )} : sec (x)

= \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

arctan (x^{3})

y = \frac{x ^{3} + 3 x ^{2} - 5 x + 2}{3}

y^{^{'}} - 8 y^{3} = 0

\int \frac{1}{2 x - 1 - 4 2 x - 1} d x

\int x^{1.1} (\frac{1}{3 x} - 1) d x

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