Home
Class 12
MATHS
Integrate the rational functions1/(x(x^...

Integrate the rational functions`1/(x(x^n+1)`[Hint: multiply numerator and denominator by `x^(n-1)`and put `x^n=t`]

Text Solution

AI Generated Solution

To solve the integral \( \int \frac{1}{x(x^n + 1)} \, dx \), we will follow the steps outlined in the hint provided. ### Step-by-step Solution: 1. **Multiply Numerator and Denominator**: We start by multiplying both the numerator and the denominator by \( x^{n-1} \): \[ \int \frac{1}{x(x^n + 1)} \, dx = \int \frac{x^{n-1}}{x^n(x^n + 1)} \, dx ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise MISCELLANEOUS EXERCISE|44 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.3|24 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.7|14 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

Integrate the rational functions (1)/(x^(4)-1)

Integrate the rational functions (1)/(x(x^(4)-1))

Integrate the rational functions x/((x+1)(x+2)

Integrate the rational functions (1)/(x^(2)-9)

Integrate the rational functions (3x-1)/((x+2)^(2))

Integrate the rational functions (1-x^(2))/(x(1-2x))

Integrate the rational functions (1)/((e^(x)-1))[ Hint : Put e^(x)=t

Integrate the rational functions (x)/((x^(2)+1)(x-1))

Integrate the rational functions (2)/((1-x)(1+x^(2)))

Integrate the rational functions (x^(3)+x+1)/(x^(2)-1)