Mathematics

Mathematics

Problem

The answers are in Chapter 24. 4. Evaluate ∫x2sin⁡(3x)dx\int x^{2} \sin (3 x) d x. (A) x2cos⁡(3x)3−2xsin⁡(3x)3−2cos⁡(3x)3+C\frac{x^{2} \cos (3 x)}{3}-\frac{2 x \sin (3 x)}{3}-\frac{2 \cos (3 x)}{3}+C (B) −x2cos⁡(3x)3+2xsin⁡(3x)3+2cos⁡(3x)3+C-\frac{x^{2} \cos (3 x)}{3}+\frac{2 x \sin (3 x)}{3}+\frac{2 \cos (3 x)}{3}+C (C) −x2cos⁡(3x)3+2xsin⁡(3x)9+2cos⁡(3x)27+C-\frac{x^{2} \cos (3 x)}{3}+\frac{2 x \sin (3 x)}{9}+\frac{2 \cos (3 x)}{27}+C (D) x2cos⁡(3x)3−2xsin⁡(3x)9−2cos⁡(3x)27+C\frac{x^{2} \cos (3 x)}{3}-\frac{2 x \sin (3 x)}{9}-\frac{2 \cos (3 x)}{27}+C (A) x2cos⁡(3x)3−2xsin⁡(3x)3−2cos⁡(3x)3+C\frac{x^{2} \cos (3 x)}{3}-\frac{2 x \sin (3 x)}{3}-\frac{2 \cos (3 x)}{3}+C (B) −x2cos⁡(3x)3+2xsin⁡(3x)3+2cos⁡(3x)3+C-\frac{x^{2} \cos (3 x)}{3}+\frac{2 x \sin (3 x)}{3}+\frac{2 \cos (3 x)}{3}+C (C) −x2cos⁡(3x)3+2xsin⁡(3x)9+2cos⁡(3x)27+C-\frac{x^{2} \cos (3 x)}{3}+\frac{2 x \sin (3 x)}{9}+\frac{2 \cos (3 x)}{27}+C (D) x2cos⁡(3x)3−2xsin⁡(3x)9−2cos⁡(3x)27+C\frac{x^{2} \cos (3 x)}{3}-\frac{2 x \sin (3 x)}{9}-\frac{2 \cos (3 x)}{27}+C

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