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Integrate the following with respect to x: ∫(1/(cos alpha + cos x))dx

Integrate the following with respect to x:
∫(1/(cos alpha + cos x))dx
 

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
3 years ago
Denominator becomes 2cos(a+x)/2*cos(a-x)/2
Now multiply and divide by sin[ (a+x)/2+(a-x)/2 ]=sina
Expanding the numerator would then give tan(a+x)/2 + tan(a-x)/2
But we obviously know the integral of tanz with respect to z is lnsecz.
Hence simply put (a+x)/2= z and (a-x)/2 = y for the first and second integral respectively.

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