CUET Preparation Today
$\int\frac{dx}{x(x^n+1)}$ is equal to : |
$\frac{1}{n}\log(\frac{x^n}{x^n+1})+C$ $\frac{1}{n}\log(\frac{x^n+1}{x^n})+C$ $\log(\frac{x^n}{x^n+1})+C$ None of these |
$\frac{1}{n}\log(\frac{x^n}{x^n+1})+C$ |
$I=\int\frac{dx}{x(x^n+1)}$ Put $x^n+1=t,nx^{n-1}dx=dt$ $I=\frac{1}{n}\int\frac{dt}{t(t-1)}=\frac{1}{n}\int(\frac{1}{t-1}-\frac{1}{t})dt=\frac{1}{n}\log(\frac{t-1}{t})+c=\frac{1}{n}\log(\frac{x^n}{x^n+1})+C$ |
