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Integrate 1/(x+1)^4

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svjr | Student, Undergraduate | (Level 2) Honors

Posted December 7, 2011 at 8:27 PM via web

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Integrate 1/(x+1)^4

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted December 7, 2011 at 9:31 PM (Answer #1)

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Use substitution to solve the integral.

You may come up with the following substitution: x+1 = t.

Differentiating the equation above you will find dx: dx = dt

Write the new integral:

`int (1/t^4)*dt = int t^(-4) dt = t^(-4+1)/(-4+1) + c`

`` Replace t by x+1.

`int dx/(x+1)^4= -1/(3(x+1)^3) + c`

Integrating`1/(x+1)^4`  yields`int dx/(x+1)^4= -1/(3(x+1)^3) + c.`

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jacqueshaw | Student | (Level 1) Honors

Posted December 9, 2011 at 2:48 AM (Answer #2)

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inverse 1/(x+1)^4

which will equal to (x+1)^-4

then int (1+x)^-4

=(1+x)^-3/-3 +c

inverse it back the faction like before which will give =1/-3(1+x)^3 +c

 

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