Question

\(\int e^{\tan x}(\tan^{7}x+5\tan^{6}x+\tan^{5}x+5\tan^{4}x)\,dx=\)

• A. \(e^{\tan x}\frac{\tan^{8}x}{8}+c\)
• B. \(e^{\tan x}(\tan^{5}x)+c\)
• C. \(e^{\tan x}\frac{\tan^{6}x}{6}+c\)
• D. \(e^{\tan x}(\tan^{7}x)+c\) \bigskip

Hint:

Look for \(e^t \cdot P(t)\) → check product rule reverse.

Answer 1

The Correct Option is A