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Integral Calculus> Please solve this ∫e x tanx(1-2sec 2 x) d...

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Please solve this∫extanx(1-2sec2x) dxI am waiting for your reply

Lovey , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:Hello student, please find answer to your question
$I = \int e^{x}.tanx(1-2sec^{2}x)dx$
$I = \int e^{x}(tanx-2sec^{2}x.tanx)dx$
$f(x) = tanx$
$f'(x) = sec^{2}x$
$f''(x) = 2sec^{2}x.tanx$
$I = \int e^{x}(f(x)-f''(x))dx$
$I = \int e^{x}(f(x)+f'(x)-f'(x)-f''(x))dx$
$I = e^{x}(f(x)-f'(x)) + constant$
$I = e^{x}(tanx-sec^{2}x) + constant$

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