Question:medium
\( \int \frac{(1 + x) e^x{\sin^2(x e^x)} dx \) is equal to:}
\( \int \frac{(1 + x) e^x{\sin^2(x e^x)} dx \) is equal to:}
Show Hint
If you see $e^x$ and $(1+x)$ in an integral, always check if $x e^x$ is your $u$! It's one of the most common substitution patterns in calculus.
Updated On: May 6, 2026
- \( -\cot(e^x) + C \)
- \( \tan(x e^x) + C \)
- \( \tan(e^x) + C \)
- \( \cot(x e^x) + C \)
- \( -\cot(x e^x) + C \)
Show Solution
The Correct Option is
Solution and Explanation
Was this answer helpful?
0
Top Questions on Methods of Integration
- The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
- MHT CET - 2025
- Mathematics
- Methods of Integration
The integral $ \int_0^1 \frac{1}{2 + \sqrt{2e}} \, dx $ is:
- MHT CET - 2025
- Mathematics
- Methods of Integration
- The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
- MHT CET - 2025
- Mathematics
- Methods of Integration
- Evaluate the integral \( \int x e^{x^2} dx \):
- BITSAT - 2025
- Mathematics
- Methods of Integration
- Want to practice more? Try solving extra ecology questions todayView All Questions
