intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb...

`intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e r ea , b in R^+)i se q u a lto` `1/(6lna^2b^3)a^(2x)b^(3x)ln(a^(2x)b^(3x))/e+k` `1/(6lna^2b^3)1/(a^(2x)b^(3x))ln1/(e a^(2x)b^(3x))+k` `1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k` `-1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k`

`(1)/(6Ina^(2)b^(3))a^(2x)b^(3x)In(a^(2x)b^(3x))/(e)+k`

`(1)/(6Ina^(2)b^(3))(1)/(a^(2x)b^(3x))In(1)/(ea^(2x)b^(3x))+k`

`(1)/(6Ina^(2)b^(3))(1)/(a^(2x)b^(3x))In(a^(2x)b^(3x))+k`

`-(1)/(6Ina^(2)b^(3))(1)/(a^(2x)b^(3x))In(a^(2x)b^(3x))+k`

Text Solution

Verified by Experts

The correct Answer is:

`I=int x((Ina^(a^(x//2)))/(3a^(5x//2)b^(3x))+(Inb^(b^(x)))/(2a^(2x)b^(4x)))dx=int(Ina^(2x)b^(3x))/(6a^(2x)b^(3x))dx `
` "Let " a^(2x)b^(3x)=t. " Then " tIna^(2)b^(3)dx=dt.`
`"Therefore, " I=int(1)/(6Ina^(2)b^(3))(Int)/(t^(2))dt`
`=(1)/(6Ina^(2)b^(3))((-Int)/(t)-int(-1)/(t^(2))dt)`
`=-(1)/(6Ina^(2)b^(3))((In et)/(t))+k`
`=-(1)/(6Ina^(2)b^(3))((Ina^(2x)b^(3x)e)/(a^(2x)b^(3x)))+k`

Topper's Solved these Questions

INDEFINITE INTEGRATION
CENGAGE|Exercise Exercise (Multiple)|17 Videos
INDEFINITE INTEGRATION
CENGAGE|Exercise Exercise (Comprehension)|17 Videos
INDEFINITE INTEGRATION
CENGAGE|Exercise Exercise 7.9|15 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

(lim)_(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x))/b) has the value equal to (a-b)/3 b. 0 c. ((a^2-b^2))/(6a^2b^2) d. (a^2-b^2)/(3a^2b^2)

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) (c) -e^x/((1+e^x)^3) (d) (-1)/((1+e^x)^3)

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

Let (b cos x)/(2 cos 2x-1)=(b + sin x)/((cos^(2) x-3 sin^(2) x) tan x), b in R . Equation has solutions if

Show that if x_(1),x_(2),x_(3) ne 0 |{:(x_(1) +a_(1)b_(1),,a_(1)b_(2),,a_(1)b_(3)),(a_(2)b_(1),,x_(2)+a_(2)b_(2),,a_(2)b_(3)),(a_(3)b_(1),,a_(3)b_(2),,x_(3)+a_(3)b_(3)):}| =x_(1)x_(2)x_(3) (1+(a_(1)b_(1))/(x_(1))+(a_(2)b_(2))/(x_(2))+(a_(3)b_(3))/(x_(3)))

CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)

If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (...
Text Solution
|
int sqrt((cosx-cos^3x)/(1-cos^(3) x)dx is equal to Option A: 2/3 si...
Text Solution
|
intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e...
Text Solution
|
int(3+2cosx)/((2+3cosx)^2)dxi se q u a lto ((sinx)/(3cosx+2))+c (b) ...
Text Solution
|
"If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))...
Text Solution
|
The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...
Text Solution
|
If int(dx)/(sqrt(sin^(3)xcos^(5)x))=a sqrt(cot x)+bsqrt(tan^(3)x)+c, t...
Text Solution
|
"I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c
Text Solution
|
If int(dx)/((x+2)(x^(2)+1)) = alog|1+x^(2)|+btan^(-1)x+ 1/5log|x+2|+C,...
Text Solution
|
Ifint(3e^x-5e^(-1))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n
Text Solution
|
If int f(x) sinx cosx dx=(1)/(2(b^(2)-a^(2))) "In " f(x)+c," then " f...
Text Solution
|
int(x^9)/((4x^2+1)^6) dx is equal to
Text Solution
|
If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h...
Text Solution
|
The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...
Text Solution
|
int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3...
Text Solution
|
If I=int (dx)/((a^(2)-b^(2)x^(2))^(3//2)), then I equals
Text Solution
|
int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= sqrt(x^2+1/(x^2)+1)+C (sqrt(x^4...
Text Solution
|
int(sqrt(x^2+1))/(x^4)dx=
Text Solution
|
int (1+2x^(6))/((1-x^(6))^(3//2))dx is equal to
Text Solution
|
The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3)) dx is equal to
Text Solution
|