Home
Class 12
MATHS
The value of int2^("mx").3^("nx")dx (whe...

The value of `int2^("mx").3^("nx")dx` (when m, `n in N`) is equal to:

A

`(2^(mx)+3^(nx))/(m" ln "2+n" ln "3)+c`

B

`(e^(m" ln "2+n" ln "3)+C)/(m" ln "2+n" ln "3)`

C

`(2^("mx").3^("nx"))/(" ln "(2^(m).3^(n))+C`

D

`((mn).2^(x).3^(x))/(m" ln "2+n" ln "3)+C`

Text Solution

Verified by Experts

BC
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise COMPREHENSION|1 Videos
  • INDEFINITE INTEGRATION

    RESONANCE|Exercise Exercise-3 Part I- JEE ADVANCED/ IIT-JEE PROBLEMS|8 Videos
  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SINGLE AND DOUBLE VALUE INTEGER TYPE|15 Videos
  • GEOMETRY

    RESONANCE|Exercise Exercise-1 (Part-I: Previous Asked Question For Pre RMO)|50 Videos
  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int a^(mx)b^(nx)dx

If m,n in N, then the value of int_(a)^(b)(x-a)^(m)(b-x)^(n)dx is equal to

Knowledge Check

  • The value of int_(0)^(pi//2n) (1)/(1+cos nx)dx , is

    A
    0
    B
    `(pi)/(4n)`
    C
    `(pi)/(2n)`
    D
    `(pi)/(2)`
  • If m and n are positive integers and f(m,n)=int_(0)^(1)x^(n-1)(logx)^(m)dx , then f(m,n) is equal to

    A
    `m/nf(m-1,n)`
    B
    `-m/nf(m-1,n)`
    C
    `n/mf(m-1,n)`
    D
    None of these
  • int_(0)^(pi//2n)(dx)/(1+(tan nx)^(n)) is equal to n in N :

    A
    `(n pi)/(4)`
    B
    `(pi)/(2n)`
    C
    `(pi)/(4n)`
    D
    `(2pi)/(n)`
  • Similar Questions

    Explore conceptually related problems

    int_(0)^(a)f(2a-x)dx=m and int_(0)^(a)f(x)dx=n then int_(0)^(2a)f(x)dx is equal to

    If one root of the equation lx^(2)+mx+n=0 is (9)/(2) equal to (l,m and n are positive integers) and (m)/(4n)=(l)/(m), then l+n is equal to

    int_(0)^(pi//2n) (dx)/(1+ cot^(n) nx) is equal to

    The value of lim_(x to 0) (e^(nx)-(1+nx+n^2/2x^2))/x^3 (n gt 0) is

    If I=int2/x(x^("lnx"))(nx)^(3)dx=Ax^("lnx"^(2))-Bx^("lnx")+C , then A/B is equal to: