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dinamix
 one year ago
what is primitive this function f(x)= 1/(x^2+1)^3..
dinamix
 one year ago
what is primitive this function f(x)= 1/(x^2+1)^3..

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3substitute \(x=\tan u\)

dinamix
 one year ago
Best ResponseYou've already chosen the best response.0i think i s very hard method

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1No, it should be quite easy knowing the identities. \( \displaystyle\large \int\limits_{ }^{ }\frac{1}{(x^2+1)^3} dx\) \(u=\tan(x)\) is a standard trig substitution. then, \(du=(\sec^2u)du\) \( \displaystyle\large \int\limits_{ }^{ }\frac{\sec^2u}{(\tan^2u+1)^3} du\) \( \displaystyle\large \int\limits_{ }^{ }\frac{\sec^2u}{(\sec^2u)^3} du\) \( \displaystyle\large \int\limits_{ }^{ }(\cos^2u) du\) then you know that: cos(2w)=cos²wsin²w cos(2w)=2cos²w1 cos(2w)+1=2cos²w ½(cos(2w)+1)=cos²w so it follows that: \( \displaystyle\large \large \frac{ 1}{ 2} \int\limits_{ }^{ } \large \left(\cos(2u)+1\right) du\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dont forget to substitute back the x.
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