Home
Class 12
MATHS
int1/(2-3x)+1/(sqrt(3x-2))\ dx...

`int1/(2-3x)+1/(sqrt(3x-2))\ dx`

Text Solution

Verified by Experts

`=int1/(2-3x)+1/(sqrt(3x-2))\ dx`

Let, `2-3x=t` and `3x-2=z`

`dx=(dt)/(-3)` and `dx=dz/3`

`=(-1)/(3)int1/(t)dt+int1/(3sqrt(z))dz`

`=(-1)/(3)ln(t)+(2sqrt(z))/(3)+C`

`=(-1)/(3)ln(2-3x)+(2sqrt(3x-2))/(3)+C`

Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos
  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

int(1)/(2-3x)+(1)/(sqrt(3x-2))dx

int(1)/(sqrt(3x-2))dx

int_(1)^(2)x sqrt(3x-2)dx

int(2x+3)/(sqrt(3x-1))dx=

Evaluate: int(x)/(sqrt(x+4))dx( ii) int(2-3x)/(sqrt(1+3x))dx

Evaluate: int1/(x^(3)sqrt(x^2-1))\ dx

int(1)/(sqrt(3x-4)-sqrt(3x-2))dx dx V3x-4-V3x-2

int1/sqrt(3-3x^2)dx

int1/sqrt(3x^2-5)dx

Evaluate the following integral: int_1^2x\ sqrt(3x-2)\ dx