COMEDK · Maths · 28. Indefinite Integration
\(\int e^x\left(1+\tan x+\tan ^2 x\right) d x \text { is equal to }\)
- A \(e^x \sin x+c\)
- B \(e^x \sec x+c\)
- C \(e^x \cos x+c\)
- D \(e^x \tan x+c\)
Answer & Solution
Correct Answer
(D) \(e^x \tan x+c\)
Step-by-step Solution
Detailed explanation
The integral is \(I = \int e^x (1 + \tan x + \tan^2 x) dx\). Using the identity \(1 + \tan^2 x = \sec^2 x\), the expression becomes \(I = \int e^x (\sec^2 x + \tan x) dx\). Let \(f(x) = \tan x\). Then \(f'(x) = \sec^2 x\). The integral is in the form…
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