Integral of 1/(x(x^n + 1)): multiply by x^(n-1) and substitute t = x^n

1. A.
   $\log(x) - \frac{1}{2}\log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.
2. B.
   $\frac{1}{2}\log(x) - \log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.
3. C.
   $\log(x) + \frac{1}{2}\log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.
4. D.
   $- \log(x) - \frac{1}{2}\log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.

Tap an option to check your answer.

1. A.
   $\ \log\left( \frac{x^{3}}{x^{3} + 1} \right) + c$, where c is the constant of integration
2. B.
   $\frac{1}{3}\log\left( \sqrt[3]{\frac{x^{3}}{x^{3} + 1}} \right) + c$, where c is the constant of integration
3. C.
   $\log\left( \sqrt[3]{\frac{x^{3}}{x^{3} + 1}} \right) + c$, where c is the constant of integration
4. D.
   $\frac{1}{3}\log\left( \frac{x^{3} + 1}{x^{3}} \right) + c$, where c is the constant of integration

Tap an option to check your answer.