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... by substitution: (a). Z x3 p x2 +2dx. (b*). Z x2 cos (x3)dx. (c). Z 1 x2 sin. 1 x dx. (d). Z cos(3x − 7) dx. (e). Z e√ x. √ x dx. (f*). Z e(x+ex) dx (use u = ex). The solution to the differential equation can be determined by multiplying both sides of the equation by an integrating factor. (d) cos(3x)sin(3x)dx. ∫ . 5. Evaluate the integral. 0 exp(2sin )cos x x dx π. ∫ . 6. Evaluate cos(2 ) x x dx π π-. ∫. As x approaches negative infinity, the value of cos ⁡ 3 x will oscillate between -1 and 1. However, the denominator, x , will become increasingly negative. This ... Yp = -9 A Cos 3x-9B Sin 3x. Plug into ODE: (-9A (os 3x-98 Sin 3x)+4(-3A Sin 3x + 3B Cos3x). + 4 CA Cos 3x + B Sin 3x). = [-5A ]. T-5. +12B Cos 3x + -12A-5B ... Apr 24, 2017 ... A more-general version of this question: "How can we sum up sin and cos series when the angles are in arithmetic progression?" Nov 21, 2023 ... ... e − 2 x cos ⁡ 3 x {\displaystyle \displaystyle -6M{{e}^{-2x}}\sin 3x+(-8M+6N){{e}^{-2x}}\cos 3x-10Mx{{e}^{-2x}}\cos 3x=2{{e}^{-2x}}\cos 3x}. ... (cos(x) In (wing)) dx. 1'(x)=-mi(3x) - 3. In (mix) + cos(3x). (3x).3. fox. +63(3X) cos x. Sari X. (6713x)) co>x. SmiX. (s) (3X). (smi x. 3 . (sm (3x)) In (smix) ... Jul 1, 2019 ... Proof Tan 3x is = Sin 3x/ Cos 3x using De Moivre's theorem · updatesvc · Steven G · Dr.Peterson · updatesvc · Steven G · updatesvc. New member. This comes from the pythagorean theorem. You can convert the sides into measurements: s1²+s2²=h². Divide each side by h², and you will see that the terms can be ...