Question

Anyone know how to do this integral?

Answer 1

\[\int\limits \frac{ x ^{2} +x+1}{ (x ^{2}+1)^{2} }dx\]

Answer 2

Play around with the fraction.

Answer 3

Maybe partial fraction decomposition

Answer 4

did you try a trig sub i think that would work just fine

Answer 5

you think i can try sin?

Answer 6

I think you can try tan

Answer 7

the hint was the x^2+1 on bottom

Answer 8

tan^2(theta)+1=sec^2(theta)

Answer 9

would the set up be integral x^2+x+1/sex^2 theta

Answer 10

well you have to replace all the x's and the dx

Answer 11

and also you are leaving off the square on bottom

Answer 12

\[x=\tan(\theta) => dx=\sec^2(\theta) d \theta \]
Replace all the x's with tan(theta)
Replace the dx with sec^2(theta) d theta

Answer 13

is it integral tan^2theta+tan theta+1/sec^2 theta d (theta)

Answer 14

If I think what you wrote is what I think then yes.

You mean the following I assume:
integral of (tan^2(theta)+tan(theta)+1)/sec^2(theta) d(theta)

Answer 15

\[\int\limits_{}^{}\frac{\tan^2(\theta)}{\sec^2(\theta)} d \theta +\int\limits_{}^{}\frac{\tan(\theta)}{\sec^2(\theta)} d \theta +\int\limits_{}^{} \frac{1}{\sec^2(\theta) }d \theta \]

Answer 16

Look at them three separately

Answer 17

\[\int\limits_{}^{}(\frac{ x^2+1 }{ (x^2+1)^2 } +\frac{ x }{ (x^2+1)^2 })*dx\]

Answer 18

\[\int\limits_{}^{}\frac{ dx }{ x^2+1 } +\int\limits_{}^{}\frac{ x }{ (x^2+1)^2 }\]

Answer 19

first one is standard formula

Answer 20

how can i figure out the answer?

Answer 21

\[\int\limits_{}^{}\frac{ x }{ (x^2+1)^2 } *dx\]
for this
x^2+1=t
2xdx=dt
xdx=dt/2

Answer 22

\[\int\limits_{}^{} \frac{ dt }{ 2*t^2 }\]

Answer 23

\[\int\limits_{}^{}\frac{ dx }{ x^2+1 } +\int\limits_{}^{}\frac{ dt }{ 2t^2 }\]

Answer 24

can u solve it @mony01

Answer 25

is it sec^2 (theta)/2(x^2+1)^2

Answer 26

I do like gorv's way.
But either way is fine.
gorv's is simpler though.

Answer 27

actual its less calculative...both ways anns will be same

Answer 28

how can i solve the rest of it?

Answer 29

What question on what part do you have?

Answer 30

\[\int\limits \frac{ dx }{ x ^{2}+1}+\int\limits \frac{ dt }{ 2t ^{2} }\]

Answer 31

the first integral is just remembering that it is acran(x)

the second one 1/2 is a constant multiple and you should know how to integrate t^(-2) at this point in calculus

Answer 32

is the answer arctan(x)-1/2(x^2+1)+C

Answer 33

Yes that's right you mean arctan(x)- 1/[2(x^2+1)] +C

good job