TS EAMCET · Maths · Indefinite Integration
\(\int e^x\left(\frac{\sec ^2 x+\tan x-\cot x}{\sin x}\right) d x=\)
- A \(e^x(\operatorname{cosec} x+\cot x)+c\)
- B \(e^x\left(\frac{\sec ^2 x+\tan x}{\sin x}\right)+c\)
- C \(e^x\left(\frac{1+\tan ^2 x}{\sin x}\right)+c\)
- D \(e^x(\operatorname{cosec} x+\sec x)+c\)
Answer & Solution
Correct Answer
(D) \(e^x(\operatorname{cosec} x+\sec x)+c\)
Step-by-step Solution
Detailed explanation
\(I=\int e^x\left(\frac{\sec ^2 x+\tan x-\cot x}{\sin x}\right) d x\) \(=\int e^x\left(\frac{\frac{1}{\cos ^2 x}+\frac{\sin x}{\cos x}-\frac{\cos x}{\sin x}}{\sin x}\right) d x\)…
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