Question:
Evaluate the following integral:
\[
\int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx
\]
Evaluate the following integral:
\[
\int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx
\]
Show Hint
When integrating products of terms with powers, consider using standard techniques like substitution or expansion to simplify the expression.
Updated On: May 15, 2025
- \( \frac{1}{6(m+1)} (2x^{3m} + 3x^{2m} + 6x^m)^{m+1} + C \)
- \( \frac{1}{6(m+1)} (2x^{3m} + 3x^{2m} + 6x^m)^{m-1} + C \)
- \( \frac{1}{6(m+1)} (2x^{3m} + 3x^{2m} + 6x^m)^{m+1} + C \)
- \( \frac{1}{6(m-1)} (2x^{3m} + mx^{2m} + 6x^m)^{m-1} + C \)
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The Correct Option is A
Solution and Explanation
The given integral involves a product of polynomials raised to a power, and can be simplified using standard integration techniques. Upon solving the integral, we arrive at the correct form of the solution.
Thus, the correct answer is option (1).
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