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16 kwi 2024 · Chapter 7 Class 12 Integrals. Serial order wise. Examples.
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Integration by parts is unnecessary. Do this $$\int \sin^3(x)\cos^2(x)\,dx = \int (1-\cos^2(x))\cos^2(x)\sin(x)\,dx $$ Let $u = \cos(x), du = -\sin(x)\,dx$ and this resolves very simply.
12 paź 2015 · Explanation: #I = int sin^3xcos^2xdx = int sin^2xcos^2xsinxdx# #I = int (1-cos^2x)cos^2xsinxdx# #cosx=t => -sinxdx=dt => sinxdx=-dt#.
8 mar 2014 · Using Werner Formulas. $$2\cos3x\sin2x=\sin (3x+2x)-\sin (3x-2x)$$. Now use $\displaystyle\int\sin mx\ dx=-\frac {\cos mx}m+C$. Finally and optionally, we can use Multiple Angle Formula to expand $\cos5x$ in the power of $\cos x$. Share.
