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Please solve this ∫e x tanx(1-2sec 2 x) dx I am waiting for your reply

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 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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