Mathematics

Mathematics

Problem

1. Evaluate ∫sin⁡19xcos⁡3xdx\int \sin ^{19} x \cos ^{3} x d x. (A) sin⁡20x20−cos⁡4x4+C\frac{\sin ^{20} x}{20}-\frac{\cos ^{4} x}{4}+C (B) sin⁡20x20−sin⁡22x22+C\frac{\sin ^{20} x}{20}-\frac{\sin ^{22} x}{22}+C (C) sin⁡20x20+sin⁡22x22+C\frac{\sin ^{20} x}{20}+\frac{\sin ^{22} x}{22}+C (D) sin⁡20x20+cos⁡4x4+C\frac{\sin ^{20} x}{20}+\frac{\cos ^{4} x}{4}+C (A) sin⁡20x20−cos⁡4x4+C\frac{\sin ^{20} x}{20}-\frac{\cos ^{4} x}{4}+C (B) sin⁡20x20−sin⁡22x22+C\frac{\sin ^{20} x}{20}-\frac{\sin ^{22} x}{22}+C (C) sin⁡20x20+sin⁡22x22+C\frac{\sin ^{20} x}{20}+\frac{\sin ^{22} x}{22}+C (D) sin⁡20x20+cos⁡4x4+C\frac{\sin ^{20} x}{20}+\frac{\cos ^{4} x}{4}+C

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