Home
Class 12
MATHS
Evaluate int x log x dx....

Evaluate ` int x log x dx`.

Text Solution

Verified by Experts

`int underset (II)(x)underset(I)(log)x dx`
`=logx {int x dx}-int {(d)/(dx)(logx)intxdx}dx`
`=(logx)(x^(2))/(2)int(1)/(x)(x^(2))/(2)dx`
`=(x^(2))/(2)log x-(1)/(2)int x dx`
`=(x^(2))/(2)logx-(1)/(2)((x^(2))/(2))+C=(x^(2))/(2)logx-(1)/(4)x^(2)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXAMPLE|18 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.1|9 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate : int e^(3 log x)dx

Evaluate: int e^x/x(x log x+1)dx

int (log x )^2 dx

Evaluate : int (e^(6log x)- e^(4logx))/(e^(3logx)- e^(log x))dx

Evaluate : int (e^(2logx)- 2e^(-3 log x) ) dx

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

Evaluate : int (e^(2logx)-e^(-log x))/(e^(2logx)-e^(logx))dx

Evaluate int (sin(ln x))/x dx

Evaluate: int_3^10[log[x]]dx

Evaluate: int(e^(x loga)+e^(a log x)) dx