Home
Class 12
MATHS
Evaluate: intx^x1n(e x)dx...

Evaluate: `intx^x1n(e x)dx`

Text Solution

Verified by Experts

The correct Answer is:
`x^(x)+C`
`I=int x^(x) " In "(ex)dx=int x^(x) (1+"In "x)dx`
` "Let "t=x^(x)=e^(x"In"x)" then " (dt)/(dx)=x^(x)(x xx (1)/(x)+"In "x)`
` or dt=x^(x)(1+"In "x)dx or I=intdt=t+C=x^(x)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.3|16 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate: inta^(x)e^(x)dx

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

Evaluate: intx^3d(tan^(-1)x)

Evaluate: int((x-1)e^x)/((x+1)^3)dx

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

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

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

Evaluate: int(e^x)/(e^(2x)+6e^x+5)dx

Evaluate: intx/((x-1)(x^2+4))dx

Evaluate: Evaluate: intx^(-11)(1+x^4)^(-1/2)dx