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The solution to the differential equation can be determined by multiplying both sides of the equation by an integrating factor. Solution. Observe that $2\cos 4x\cos x = \cos 5x + \cos 3x$ by the sum-to-product formulas. Defining $a = \cos 3x$ and $b = \cos 5x$ , we have $a^3 + b^3 ... x + cos(3x) f(x) = sin(tan( p sin(x))) f(x) = etan(x3) + ln(sin(. / x)). Use Logarithmic Differentiation to find the following derivatives with respect to x ... Dec 15, 2016 ... ... integrals: a. J 1+x-3 - ~ +e= +cos(3x) +1['2 b. JxV x2 +1 dx c. JxJX+I dx. 1~x cos(x) - sin x d e. 2 x. ,.,. X. 4". Page 4. 4. Sketch the curve ... < Sux, cos 3x >. = -H. This stooks that as 3+. =0. 0 other. Fucher in V. F(I = 6) ... cos 3x unti. Vo es x)dx = 0. Page 2. (iv) the. ORTHOGONAL PROJECTION. PCA ... ... 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). Apr 4, 2020 ... cos(x) cos(2x) cos(3x)···cos(nx)dx = 0? Problem 3. Suppose that k and n are positive integers, a1,a2,...,ak ∈ {1,2,...,n} and b1,b2 ... (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-. ∫. Differentiate wrt x \sin(x)\left(121\left(\sin(x)\right)^{2}\left(\cos(x)\right)^{4}-75\left(\cos(x)\right)^{2}\left(\sin(x)\right)^{ PROBLEM SHEET 11. 11.1 Integrate cos(3x + 4). 11.2 Integrate (1 − 2x)10. 11.3 Integrate e4x-1. 11.4 Integrate (4x + 3)-1. 11.5 Find the equation of the ...