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Problem Determine ∫ x sin ( 3 x + π 4 ) d x \displaystyle \int x\sin\!\left(3x+\dfrac{\pi}{4}\right)\,dx ∫ x sin ( 3 x + 4 π ) d x − x 3 cos ( 3 x + π 4 ) − 1 9 sin ( 3 x + π 4 ) + C -\dfrac{x}{3}\cos\!\left(3x+\dfrac{\pi}{4}\right)-\dfrac{1}{9}\sin\!\left(3x+\dfrac{\pi}{4}\right)+C − 3 x cos ( 3 x + 4 π ) − 9 1 sin ( 3 x + 4 π ) + C − x 3 sin ( 3 x + π 4 ) + 1 9 cos ( 3 x + π 4 ) + C -\dfrac{x}{3}\sin\!\left(3x+\dfrac{\pi}{4}\right)+\dfrac{1}{9}\cos\!\left(3x+\dfrac{\pi}{4}\right)+C − 3 x sin ( 3 x + 4 π ) + 9 1 cos ( 3 x + 4 π ) + C − x 3 cos ( 3 x + π 4 ) + 1 9 sin ( 3 x + π 4 ) + C -\dfrac{x}{3}\cos\!\left(3x+\dfrac{\pi}{4}\right)+\dfrac{1}{9}\sin\!\left(3x+\dfrac{\pi}{4}\right)+C − 3 x cos ( 3 x + 4 π ) + 9 1 sin ( 3 x + 4 π ) + C − x 3 cos ( 3 x + π 4 ) + 1 6 sin ( 3 x + π 4 ) + C -\dfrac{x}{3}\cos\!\left(3x+\dfrac{\pi}{4}\right)+\dfrac{1}{6}\sin\!\left(3x+\dfrac{\pi}{4}\right)+C − 3 x cos ( 3 x + 4 π ) + 6 1 sin ( 3 x + 4 π ) + C Browse the problem library