Home
Class 12
MATHS
Evaluate: int((1-xsinx)dx)/(x(1-x^3e^(3c...

Evaluate: `int((1-xsinx)dx)/(x(1-x^3e^(3cosx)))`

Text Solution

Verified by Experts

Here, `I=int((1-xsinx)dx)/(x(1-(x e^(cosx))^(3)))`
Put `xe^(cosx)=t " so that " (xe^(cosx)(-sinx)+e^(cosx))dx=dt`
` :. I=int(dt)/(t(1-t^(3)))=int(dt)/(t^(4)((1)/(t^(3))-1))`
Let `(1)/(t^(3))-1=y " or " dy=(-3)/(t^(4))dt`
` :. I=(1)/(3)int (dy)/(y)=-(1)/(3)log|y|+C= -(1)/(3)log|(1)/(t^(3))-1|+C`
`= -(1)/(3)log_(e)|(1)/(x^(3)e^(3cosx))-1|+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.1|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.2|7 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|2 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE ENGLISH|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(1-sinx)/(x+cosx)dx

Evaluate: inte^x((1-sinx)/(1-cosx))dx

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

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

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

Evaluate: int(x+1+e^x)\ dx

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

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

Evaluate int(x+sinx)/(1+cosx)dx

Evaluate: int1/(13+3cosx+4sinx)dx