How do you integrate $int ( 1/((x+1)^2+4)) dx$ using partial fractions?

Question

How do you integrate $int ( 1/((x+1)^2+4)) dx$ using partial fractions?

1 Answer

Impact of this question

4533 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-09T04:13:50

$1/2arctan((x+1)/2)+C$

Explanation:

$I=int1/((x+1)^2+4)dx$

This isn't a job for partial fractions, it's a job for a trig substitution. Let $x+1=2tantheta$ . This implies that $dx=2sec^2thetad theta$ . Substituting in tells us:

$I=int1/(4tan^2theta+4)(2sec^2thetad theta)=1/2intsec^2theta/(1+tan^2theta)d theta$

Since $1+tan^2theta=sec^2theta$ :

$I=1/2intd theta=1/2theta+C$

Undoing the substitution $x+1=2tantheta$ :

$I=1/2arctan((x+1)/2)+C$

Science

Math

Humanities

... and beyond

How do you integrate $int ( 1/((x+1)^2+4)) dx$ using partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you integrate int ( 1/((x+1)^2+4)) dxint ( 1/((x+1)^2+4)) dx using partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you integrate $int ( 1/((x+1)^2+4)) dx$ using partial fractions?