Home
Class 12
MATHS
Evaluate int(log(e)x)^(2)dx...

Evaluate `int(log_(e)x)^(2)dx`

Text Solution

Verified by Experts

The correct Answer is:
`x*(log_(e)x)^(2)-2(xlog_(e)x-x)+c `
`int 1*(log_(e)x)^(2)dx`
`=x*(log_(e)x)^(2)-int 2(log_(e)x)/(x)*xdx `
`=x*(log_(e)x)^(2)-2int log_(e)xdx `
`=x*(log_(e)x)^(2)-2(xlog_(e)x-x)+c `
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise EXERCISES (Single Correct Answer Type)|77 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise Exercises (Multiple Correct Answers Type)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.8|7 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE ENGLISH|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate int 5^(log _(e)x)dx

Evaluate int 2^(log_(4)x)dx

int((log _(e)x)^(3))/(x)dx

Evaluate : int(log_(e)(1+sin^(2)x))/(cos^(2)x)dx

Evaluate int(1+x^(2)log_(e)x)/(x+x^(2)log_(e)x)dx

Evaluate int(log_(e)(x+sqrt(x^(2)+1)))/(sqrt(x^(2)+1))dx.

Evaluate int(log_(e)(x+sqrt(x^(2)+1)))/(sqrt(x^(2)+1))dx.

Evaluate : int ((1+"log"x)^(2))/(x)-" dx "

int log_(e)(a^(x))dx=

Evaluate: int(log(logx)/x)\ dx