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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2018 · Mathematics · Indefinite Integration

What is ∫ e^ In( x) d x equal to? Where c is the constant of...

What is ∫eIn⁡(tan⁡x)dx\int e^{\operatorname{In}(\tan x)} d x equal to? Where c is the constant of integration.

Options

  1. AIn ∣tan⁡x∣+c|\tan x|+c
  2. BIn ∣sec⁡x∣+c|\sec x|+c
  3. Ctan⁡x+c\tan x+c
  4. Detan⁡x+ce^{\tan x}+c

Correct answer

B. In ∣sec⁡x∣+c|\sec x|+c

Step-by-step solution

∫eln⁡(tan⁡x)dx=∫tan⁡xdx=ln⁡∣sec⁡x∣+c\begin{aligned} & \int e^{\ln (\tan x)} d x=\int \tan x d x \\ & =\ln |\sec x|+c\end{aligned}
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