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|Exercise Competition level Questions|76 Videos

  • INTEGRALS

    AAKASH INSTITUTE|Exercise Objective Type Questions (Only one answer)|64 Videos

  • DIFFERENTIAL EQUATIONS

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

  • INVERSE TRIGONOMETRIC FUNCTIONS

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

Similar Questions

Explore conceptually related problems

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

Evaluate the following: (i) int sqrt(1+sin((1)/(2)x))dx (ii) int(x^(2))/(sqrt(1-x))dx

Evaluate the following (i) int x log (1+x) dx (ii) int x log^2x dx

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

inte^(x)(1-sinx)/(1-cosx)dx=

int(cos2x)/(sinx+cosx)dx=

Evaluate: (i) int(sin^(2)x)/(1+cos x)dx (ii) int(sec^(2)x+cos ec^(2)x)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 the following integrals: (i) int_2^3 x^2 dx (ii) int_1^3 x/((x+1)(x+2)) dx