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Find the integral ∫(1/x(x n +1))dx

Find the integral
∫(1/x(xn+1))dx

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:Hello student, please find answer to your question
I = \int \frac{1}{x(x^{n}+1)}dx
I = \int \frac{x^{n-1}}{x(x^{n}+1).x^{n-1}}dx
I = \int \frac{x^{n-1}}{x^{n}(x^{n}+1)}dx
x^{n}+1 = t
nx^{n-1}dx = dt
I = \int \frac{1}{t(t-1)}.\frac{dt}{n}
I = \frac{1}{n}\int (\frac{1}{t-1}-\frac{1}{t})dt
I = \frac{1}{n}ln|\frac{t-1}{t}| + c
I = \frac{1}{n}ln|\frac{x^{n}}{x^{n}+1}| + c

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