What is the integral of (cos^3(w))/(cos^4(w)) ?

The integral of (cos^3(w))/(cos^4(w)) is ln|tan(w)+sec(w)|+C

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integral of (cos^3(w))/(cos^4(w))

\int \frac{cos ^{3} ( w )}{cos ^{4} ( w )} d w

ln ∣ tan (w) + sec (w) ∣ + C

Solution steps

\int \frac{cos ^{3} ( w )}{cos ^{4} ( w )} d w

Simplify

\frac{cos ^{3} ( w )}{cos ^{4} ( w )} : sec (w)

= \int sec (w) d w

Use the common integral:

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

= ln ∣ tan (w) + sec (w) ∣

Add a constant to the solution

= ln ∣ tan (w) + sec (w) ∣ + C

What is the integral of (cos^3(w))/(cos^4(w)) ?
The integral of (cos^3(w))/(cos^4(w)) is ln|tan(w)+sec(w)|+C