dinamix
  • dinamix
what is primitive this function f(x)= 1/(x^2+1)^3..
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

ganeshie8
  • ganeshie8
substitute \(x=\tan u\)
dinamix
  • dinamix
i think i s very hard method
SolomonZelman
  • SolomonZelman
No, 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)=cos²w-sin²w cos(2w)=2cos²w-1 cos(2w)+1=2cos²w ½(cos(2w)+1)=cos²w so it follows that: \( \displaystyle\large \large \frac{ 1}{ 2} \int\limits_{ }^{ } \large \left(\cos(2u)+1\right) du\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

SolomonZelman
  • SolomonZelman
dont forget to substitute back the x.

Looking for something else?

Not the answer you are looking for? Search for more explanations.