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Problem Determine ∫ x 3 cos 2 x d x \displaystyle \int x^{3}\cos 2x\,dx ∫ x 3 cos 2 x d x 1 2 x 3 sin 2 x − 3 4 x 2 cos 2 x − 3 4 x sin 2 x + 3 8 cos 2 x + C \tfrac12 x^{3}\sin 2x - \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x + \tfrac38 \cos 2x + C 2 1 x 3 sin 2 x − 4 3 x 2 cos 2 x − 4 3 x sin 2 x + 8 3 cos 2 x + C 1 2 x 3 sin 2 x + 3 4 x 2 cos 2 x − 3 4 x sin 2 x + C \tfrac12 x^{3}\sin 2x + \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x + C 2 1 x 3 sin 2 x + 4 3 x 2 cos 2 x − 4 3 x sin 2 x + C 1 2 x 3 sin 2 x + 3 4 x 2 cos 2 x − 3 4 x sin 2 x − 3 8 cos 2 x + C \tfrac12 x^{3}\sin 2x + \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x - \tfrac38 \cos 2x + C 2 1 x 3 sin 2 x + 4 3 x 2 cos 2 x − 4 3 x sin 2 x − 8 3 cos 2 x + C 1 4 x 3 sin 2 x + 3 4 x 2 cos 2 x − 3 4 x sin 2 x − 3 8 cos 2 x + C \tfrac14 x^{3}\sin 2x + \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x - \tfrac38 \cos 2x + C 4 1 x 3 sin 2 x + 4 3 x 2 cos 2 x − 4 3 x sin 2 x − 8 3 cos 2 x + C Browse the problem library