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evaluate the following integral ∫ sec x / sec 2x dx

evaluate the following integral
∫ sec x / sec 2x dx

Grade:12

1 Answers

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

I = \int \frac{secx}{sec2x}dx
I = \int \frac{cos2x}{cosx}dx
I = \int \frac{2cos^{2}x-1}{cosx}dx
I = \int 2cosxdx - \int secxdx
I = 2sinx - \int secxdx
I_{1} = \int secxdx
I_{1} = \int \frac{secx(secx+tanx)}{secx+tanx}dx
secx+tanx = t
(secxtanx+sec^{2}x)dx = t
I_{1} = \int \frac{1}{t}dt
I_{1} = log(t) + c
I_{1} = log(secx+tanx) + c
I = 2sinx - log(secx+tanx) + c

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