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Grade 12Integral Calculus

evaluate
∫ tan x / sec x + tan x dx

Profile image of taniska
11 Years agoGrade 12
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1 Answer

Profile image of Jitender Singh
11 Years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{tanx}{secx+tanx}dx
I = \int \frac{tanx(secx-tanx)}{(secx+tanx)(secx-tanx)}dx
I = \int \frac{secxtanx-tan^2x}{sec^2x-tan^2x}dx
I = \int \frac{secxtanx-tan^2x}{1}dx
I = \int secxtanxdx-\int tan^2xdx
I = \int secxtanxdx-\int (sec^2x-1)dx
I = \int secxtanxdx-\int sec^2xdx+\int dx
I =secx-tanx+x+c