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Grade 11Integral Calculus

Find the integral
∫(1/x(xⁿ+1))dx

Kawal

12 Years agoGrade 11

1 Answer

Jitender Singh

Approved Tutor Answer12 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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