Home
Class 12
MATHS
Evaluate: inte^x(x^2+1)/((x+1)^2)\ dx...

Evaluate: `inte^x(x^2+1)/((x+1)^2)\ dx`

Text Solution

Verified by Experts

We have `I=inte^(x)*((x^(2)+1))/((x+1)^(2))dx=inte^(x)*{((x+1)^(2)-2x)/((x+1)^(2))}dx`
`=inte^(x)*{1-(2x)/((x+1)^(2))}dx=inte^(x)dx-2int*(x)/((x+1)^(2))dx`
`=e^(x)-2*inte^(x)*({(x+1)-1})/((x+1)^(2))dx=e^(x)*{(1)/((x+1))-(1)/((x+1)^(2))}dx`
`=e^(x)-2*inte^(x){f(x)+f'(x)}dx,"where"f(x)=(1)/((x+1))andf'(x)=(-1)/((x+1)^(2))`
`=e^(x)-2e*f(x)+C=e^(x)-2e^(x).(1)/((x+1))+C`
`=e^(x)*{1-(2)/((x+1))}+C=e^(x)((x-1)/(x+1))+C`.
Promotional Banner

Topper's Solved these Questions

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise EXERCISE 13A VERY SHORT ANSWER QUESTIONS|10 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise EXERCISE 13A SHORT ANSWER QUESTIONS|92 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5F|21 Videos

  • PROBABILITY

    RS AGGARWAL|Exercise Exercise 29 B|2 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

Evaluate: int(x^(2)+3x+1)/((x+1)^(2))dx

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

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

Evaluate: inte^x(1/x-1/x^2)dx

Evaluate: int(x^(2)+x+1)/((x-1)^(3))dx