121616949-math.169 - 8 Techniques of Integration Over the...

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8 Techniques of Integration Over the next few sections we examine some techniques that are frequently successful when seeking antiderivatives of functions. Sometimes this is a simple problem, since it will be apparent that the function you wish to integrate is a derivative in some straightforward way. For example, faced with Z x 10 dx you realize immediately that the derivative of x 11 will supply an x 10 : ( x 11 ) = 11 x 10 . We don’t want the “11”, but constants are easy to alter, because differentiation “ignores” them
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Unformatted text preview: in certain circumstances, so d dx 1 11 x 11 = 1 11 11 x 10 = x 10 . From our knowledge of derivatives, we can immediately write down a number of an-tiderivatives. Here is a list of those most often used: Z x n dx = x n +1 n + 1 + C, if n ± =-1 Z x-1 dx = ln | x | + C Z e x dx = e x + C 155...
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