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integrate the following integral ∫ 1 / 1 + sec ax dx

 
integrate the following integral
∫ 1 / 1 + sec ax dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{1}{1+secax}dx
I = \int \frac{cosax}{1+cosax}dx
I = \int \frac{1+cosax-1}{1+cosax}dx
I = \int dx-\int \frac{1}{1+cosax}dx
I = x-\int \frac{1}{2cos^{2}\frac{ax}{2}}dx
I = x-\int \frac{sec^{2}\frac{ax}{2}}{2}dx
I = x-\frac{tan\frac{ax}{2}}{2.\frac{a}{2}}+c
I = x-\frac{tan\frac{ax}{2}}{a}+c

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