Integrate 1/(x(xⁿ + 1)) with respect to x.1/(x(xⁿ + 1)) का x के सापेक्ष समाकलन कीजिए।

Explanation

Write the integrand as xⁿ⁻¹/(xⁿ(xⁿ + 1)) and put t = xⁿ (dt = nxⁿ⁻¹dx). The integral becomes (1/n)∫dt/(t(t + 1)) = (1/n) log|t/(t + 1)| + c = (1/n) log|xⁿ/(xⁿ + 1)| + c.समाकल्य को xⁿ⁻¹/(xⁿ(xⁿ + 1)) लिखें और t = xⁿ रखें (dt = nxⁿ⁻¹dx)। तब समाकल (1/n)∫dt/(t(t + 1)) = (1/n) log|t/(t + 1)| + c = (1/n) log|xⁿ/(xⁿ + 1)| + c हो जाता है।