Home
Class 12
MATHS
Evaluate following : (i) inte^(x){sinx...

Evaluate following :
`(i) inte^(x){sinx+cosx}dx`
`(ii) inte^(x)(x^(2)+1)/((x+1)^(2)}dx`

Text Solution

Verified by Experts

`(i) l=ine^(x){sinx+cosx}dx`
Consider , `f(x)=sinximpliesf'(x)=cosx`
`impliesl=inte^(x){sinx+cosx}dx`
`=e^(x)sinx+C`
`(ii) l=inte^(x){(x^(2)+1)/((x+1)^(2))}dx`
`l=inte^(x){(x^(2)-1+2)/((x+1)^(2))}dx`
`=inte^(x){(x^(2)-1)/((x+1)^(2))+(2)/((x+1)^(2))}dx`
`:.l=inte^(x){(x-1)/(x+1)+(2)/((x+1)^(2))}dx`
Consider `f(x)=(x-1)/(x+1)impliesf'(x)=(2)/((x+1)^(2))`
`:.l=inte^(x){(x-1)/(x+1)+(2)/((x+1)^(2))}dx`
`=e^(x){(x-1)/(x+1)}+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Competition level Questions|80 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (Only one answer)|70 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

int(x-sinx)/(1-cosx)dx

int(x-sinx)/(1-cosx)dx

inte^(x)(cosx-sinx)dx

Evaluate the following: i) int(xcosx-sinx)/(xsinx) dx, ii) int((x/(x+1)-In(x+1))/(x(In(x+1))))dx

Evaluate: (i) int(sinx)/(1+cos^2x)\ dx (ii) int(2x^3)/(4+x^8)\ dx

Evaluate: (i) int(sinx)/(1+cos^2x)\ dx (ii) int(2x^3)/(4+x^8)\ dx

(i)intsec^(7) x. sin x dx" "(ii) int(1)/(sinx. cos^(2) x)dx

Evaluate the following : (i) int(x+2)/((x+3)(x+4)^((3)/(2))dx (ii) int((x+3)/(2x+5))^((1)/(2))*(1)/(x)dx

Evaluate the following : (i) int(x+(1)/(x))^(3//2)((x^(2)-1)/(x^(2)))dx " (ii) " int(sqrt(2+logx))/(x)dx (iii) int((sin^(-1)x)^(3))/(sqrt(1-x^(2)))dx " (iv) " int(cotx)/(sqrt(sinx))dx

Evaluate: (i) int(sin^2x)/(1+cosx)\ dx (ii) int(sec^2x+cos e c^2x)\ dx