lunes, 9 de mayo de 2011

More Examples of Integral by Substitution



$\int u\;du=\frac{u^2}{2}+C$


$\int sinx*cosx\;dx$
$u= sinx$
$du= cosxdx$
$\int u\;du= \frac{1}{2} u^2+c$
$\frac{1}{2} sin^2x+c$


$\int sin^2 3x\cos 3x\;dx$
$u= 3x$
$du= 3dx$
$\frac{1}{3}du= dx$
$\frac{1}{3}\int sin^2 u\cos u\;du$
$u= sin u$
$du= cos u\;du$
$\frac{1}{3}\int u^2\;du = \frac{1}{3}\;(\frac{1}{3}u^3)+c$


$\int e^x(1+e^x)^{10}\;dx$
$u= 1+e^x$
$du= e^x\;dx$
$\int u^{10}\;du$


$\int \frac{(lnx)^2}{x}\;dx$
$u= lnx$
$du= \frac{1}{x}\;dx$
$\int u^2\;du$


$$\int \frac{1}{2x-1}\;dx$$

$$u= 2x-1$$

$$du= 2dx$$


$$\frac{1}{2}\int \frac{1}{u}\;du$$



8 comentarios:

  1. What program do you use to write those equations down?

  2. I used a script called mathjax. If you whant to use it tell and I show you how

  3. Why? Why would anyone make a blog talking about integrals? I don't suppose you'll be doing Taylor series and 3d integrals now, will ya?

  4. Let's see what he will be posting in the future :P