# Integrate 1/(x+1)^4

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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.` **

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