dux 3,142 Posted October 22, 2017 Share Posted October 22, 2017 how to find the integral of (x^2 + 3)/(x^2 +1)? steps would be great Link to comment Share on other sites More sharing options...
ZikyungDerp 3,644 Posted October 22, 2017 Share Posted October 22, 2017 Uhhh.. I'd help but this is about the extent of what I'd be able to do mathwise Link to comment Share on other sites More sharing options...
dux 3,142 Posted October 22, 2017 Author Share Posted October 22, 2017 Uhhh.. I'd help but this is about the extent of what I'd be able to do mathwise id slay my midterm wit this. too bad we arent allowed calculators Link to comment Share on other sites More sharing options...
chanychanchan 3,203 Posted October 22, 2017 Share Posted October 22, 2017 if all else fails do integration by parts Link to comment Share on other sites More sharing options...
dux 3,142 Posted October 22, 2017 Author Share Posted October 22, 2017 if all else fails do integration by parts wish i knew what that is Link to comment Share on other sites More sharing options...
chanychanchan 3,203 Posted October 22, 2017 Share Posted October 22, 2017 wish i knew what that is do you have a way to check the answer? (i cant be absolutely sure either asdfgh) Link to comment Share on other sites More sharing options...
Wasta 5,874 Posted October 22, 2017 Share Posted October 22, 2017 Turn (x^2 + 3)/(x^2 +1) into: [(x^2 +3) - (x^2 +1)]/(x^2 + 1) + 1 Simplify: 2/(x^2 +1) + 1 Take antiderivative to get: 2arctan(x) + x + C Link to comment Share on other sites More sharing options...
27lines 781 Posted October 22, 2017 Share Posted October 22, 2017 I would try polynomial long division. The theoretical guarantee is that you can write this in the form (A/(x^2+1)) + Bx + C, and that you can integrate if you know the derivative of arctan. Link to comment Share on other sites More sharing options...
dux 3,142 Posted October 22, 2017 Author Share Posted October 22, 2017 do you have a way to check the answer? (i cant be absolutely sure either asdfgh) yeah thank gawd Turn (x^2 + 3)/(x^2 +1) into: [(x^2 +3) - (x^2 +1)]/(x^2 + 1) + 1 Simplify: 2/(x^2 +1) + 1 Take antiderivative to get: 2arctan(x) + x + C oh thank you sm! did you just have the antiderivative memorized? I would try polynomial long division. The theoretical guarantee is that you can write this as (A/(x^2+1)) + Bx + C, and that you can integrate. i tried but got stuck after dividing. i didnt know how to integrate 1/(x^2 +1) Link to comment Share on other sites More sharing options...
Wasta 5,874 Posted October 22, 2017 Share Posted October 22, 2017 yeah thank gawd oh thank you sm! did you just have the antiderivative memorized? Yep, if you use trig antiderivatives enough you'll be able to recognize the form quickly Link to comment Share on other sites More sharing options...
Recommended Posts
Archived
This topic is now archived and is closed to further replies.