Home
Class 12
MATHS
"If " int(5tanx)/(tanx-2)dx=x+a " ln"(si...

`"If " int(5tanx)/(tanx-2)dx=x+a " ln"(sinx-2cosx)+k " then " a= `

A

-1

B

-2

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
` int(5tanx)/(tanx-2)dx=int(5sinx)/(sinx-2cosx)dx`
`=int((sinx-2cosx)+2(cosx+2sinx))/((sinx-2cosx))dx`
`=int dx+2int(cosx+2sinx)/(sinx-2cosx)dx`
`=x+2 " In"|(sinx-2cosx)|+k`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Single Correct Answer Type|48 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Numerical)|10 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int(tanx)/(secx+tanx)dx=

If the integral int(5tanx)/(tanx-2)dx = x+a"ln"|sinx-2cosx|+k , then a is equal to:

Knowledge Check

  • inte^(x)tanx(1+tanx)dx=

    A
    `e^(x)(tanx-1)+c`
    B
    `e^(x)(tanx+1)+c`
    C
    `e^(-x)(tanx-1)+c`
    D
    `e^(x)(sec^(2)x-1)+c`

  • If int (5tanx)/(tan x-2) dx=x+alpha In |sin x-2 cos x|+k, then a is equal to

    A
    `-1`
    B
    `-2`
    C
    1
    D
    2

  • If the integral int(5tanx)/(tanx-2)dx = x + a log [sinx-2 cos x]+k then a is equal to

    A
    `-1`
    B
    `-2`
    C
    1
    D
    2

    • Similar Questions

    Explore conceptually related problems

    int(tanx)/((1-sinx))dx

    int(tanx)/(1+cosx)dx=

    If the integral int (5 tanx)/(tanx-2) dx=x+a log |sin x-2 cosx|+c , then a is equal to

    int2^(tanx)/(cos^2x)dx

    int((1-tanx)/(1+tanx))^(2)dx=

    Home
    Profile