Integrate 1/(x+1)^4 Solution 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.].

1. Integrate 1/(x+1)^4
Solution
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.]