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Integral Calculus> evaluate ∫ tan x / sec x + tan x dx...

question mark

evaluate
∫ tan x / sec x + tan x dx

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

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

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