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Question
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
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Solution
`int cosx/(cos(x - "a")) "d"x`
Put `x - "a"` = u
x = `"u" + "a"`
dx = du
`int cosx/(cos(x - "a")) "d"x = int (cos("u" + "a"))/(cos "u") "du"`
= `int (cos "u" cos "a" - sin "u" sin "a")/(cos "u") "du"`
= `int ((cos "u" cos "a")/(cos "u") - (sin"u" sin"a")/cos"u") "du"`
= `int cos "a" " du" - int tan "u" sin "a" * "du"`
= `cos "a" int "du" - sin "a" int tan "u" "du"`
= `cos "a"("u") - sin "a" log |sec "u"| + "c"`
`int cosx/(cos(x - "a")) "d"x = (x - "a") cos"a" - sin"a" log|sec(x - "a")| + "c"`
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