TS EAMCET · Maths · Indefinite Integration
If \(\int e^x(1+x) \cdot \sec ^2\left(x e^x\right) d x\) \(=f(x)+\) constant, then \(f(x)\) is equal to
- A \(\cos \left(x e^x\right.\)
- B \(\sin \left(x e^x\right.\)
- C \(2 \tan ^{-1}(x)\)
- D \(\tan \left(x e^x\right)\)
Answer & Solution
Correct Answer
(D) \(\tan \left(x e^x\right)\)
Step-by-step Solution
Detailed explanation
Given that, \[ \int e^x(1+x) \cdot \sec ^2\left(x e^x\right) d x=f(x)+\text { constant } \] Put \[ x e^x=t \text { in LHS } \]…
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