Math  /  Calculus

QuestionProblem 2. (1 point) Evaluate the following integral. Use substitution if necessary. Remember to write your answer in terms of the original variable (x)(x). x(8+x2)5dx=112(8+x2)6+C\int x\left(8+x^{2}\right)^{5} d x=\frac{1}{12}\left(8+x^{2}\right)^{6}+C

Studdy Solution
Verify the integration result by differentiating 112(8+x2)6+C\frac{1}{12} (8 + x^2)^6 + C with respect to xx and checking if it equals the original integrand x(8+x2)5x(8 + x^2)^5.
The differentiation process should confirm the correctness of the integration.
The evaluated integral is:
x(8+x2)5dx=112(8+x2)6+C \int x(8 + x^2)^5 \, dx = \frac{1}{12} (8 + x^2)^6 + C

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