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Answer 1 · 2017-01-09T15:13:34

#int(4 - 5sin(x))/(cos^2(x))dx = 4tan(x) - 5sec(x) + C#

Given: #int(4 - 5sin(x))/(cos^2(x))dx#

Use the identities #1/cos(x) = sec(x) and tan(x) = sin(x)/cos(x)#:

#int(4sec^2(x) - 5tan(x)sec(x))dx#

Break the integral into two integrals:

#4intsec^2(x)dx - 5inttan(x)sec(x)dx#

Both of these are well known:

#4tan(x) - 5sec(x) + C#