integral of sin 3 2x cos 4 2x dx How do you find the integral of cos4 2x sin3 2x Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Eddie Jul 15 2016 1 10cos5 2x 1 14cos7 2x sin 2x C Explanation cos4 2x sin3 2x cos4 2x
int e x cos x dx int cos 3 x sin x dx int frac 2x 1 x 5 3 int 0 pi sin x dx int a b x 2dx int 0 2 pi cos 2 theta d theta partial fractions int 0 1 frac 32 x 2 64 dx substitution int frac e x e x e x dx u e x Show More The Integral Calculator lets you calculate integrals and antiderivatives of functions online for free Our calculator allows you to check your solutions to calculus exercises It helps you practice by showing you the full working step by step integration
integral of sin 3 2x cos 4 2x dx
integral of sin 3 2x cos 4 2x dx
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Solve your math problems using our free math solver with step by step solutions Our math solver supports basic math pre algebra algebra trigonometry calculus and more Answer link 1 8 cos 4 2x C start by noticing that from the power and chain rules d dx cos 4 2x 4 cos 3 2x sin 2x 2 8 cos 3 2x sin 2x and so your integral is actually int d dx 1 8 cos 4 2x dx 1 8 int d dx cos 4 2x dx 1 8
lim x to 3 frac 5x 2 8x 13 x 2 5 lim x to 0 frac sin x x int e x cos x dx int cos 3 x sin x dx int 0 pi sin x dx frac d dx frac 3x 9 2 x frac d 2 dx 2 frac 3x 9 2 x implicit derivative frac dy dx x y 2 x y 1 int cos 2x dx frac12 sin 2x C nonumber int cos 2 2x dx int frac 1 cos 4x 2 dx frac12 big x frac14 sin 4x big C nonumber Finally we rewrite cos 3 2x as cos 3 2x cos 2 2x cos 2x big 1
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What is the integral of cos 3 2x sin 4 2x The integral of cos 3 2x sin 4 2x is 1 2 sin 5 2x 5 sin 7 2x 7 C Integrals of the form sin mx sin nx dx cos mx cos nx dx and sin mx cos nx dx
I ORI sin3 2xdx 1 2 sin2 2xd cos 2x 1 2sin2 2x cos 2x 1 2 4 sin 2xcos2 2xdx 1 2sin2 2x cos 2x 2 sin 2x 1 sin2 2x dx 1 2sin2 2x cos 2x 2 sin 2xdx 2I cos 2x 6 sin2 2x 2 C 1 6cos3 2x 1 2cos 2x C I sin 3 1 Answer Morgan Dec 24 2016 sin4 x cos2 x x 16 sin 4x 64 sin3 2x 48 C Explanation This integral is pretty tricky It s going to require the use of a few trigonometric identities and rules for integration I ll include definitions or explanations of the rules
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integral of sin 3 2x cos 4 2x dx - Consider the integral I xsinx 1 cos 2x dx x 0 i Express I 2 sinx 1 cos 2x dx x 0 ii Show that I 2 4