English

Integrate the following with respect to the respective variable : (6x+5)32 - Mathematics and Statistics

Advertisements
Advertisements

Question

Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`

Sum
Advertisements

Solution

`int (6x + 5)^(3/2*dx`

= `((6x + 5)^(3/2))/(6 xx 5/2) + c`

= `(1)/(15)(6x + 5)^(5/2) + c`.

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 150]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 2.3 | Page 150

RELATED QUESTIONS

Find: `I=intdx/(sinx+sin2x)`


Integrate the rational function:

`x/((x + 1)(x+ 2))`


Integrate the rational function:

`(1 - x^2)/(x(1-2x))`


Integrate the rational function:

`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]


Integrate the rational function:

`1/(e^x -1)`[Hint: Put ex = t]


`int (xdx)/((x - 1)(x - 2))` equals:


Find `int(e^x dx)/((e^x - 1)^2 (e^x + 2))`


Find : 

`∫ sin(x-a)/sin(x+a)dx`


Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`


Integrate the following w.r.t. x : `x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))`


Integrate the following w.r.t. x : `(x^2 + x - 1)/(x^2 + x - 6)`


Integrate the following w.r.t. x : `(2x)/((2 + x^2)(3 + x^2)`


Integrate the following w.r.t. x : `(5x^2 + 20x + 6)/(x^3 + 2x ^2 + x)`


Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`


Integrate the following w.r.t. x : `(1)/(x^3 - 1)`


Integrate the following w.r.t. x: `(2x^2 - 1)/(x^4 + 9x^2 + 20)`


Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`


Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`


Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`


Evaluate:

`int (2x + 1)/(x(x - 1)(x - 4)) dx`.


Evaluate: `int "3x - 2"/(("x + 1")^2("x + 3"))` dx


State whether the following statement is True or False.

If `int (("x - 1") "dx")/(("x + 1")("x - 2"))` = A log |x + 1| + B log |x - 2| + c, then A + B = 1.


`int sqrt(4^x(4^x + 4))  "d"x`


`int 1/(2 +  cosx - sinx)  "d"x`


`int "e"^x ((1 + x^2))/(1 + x)^2  "d"x`


`int (3x + 4)/sqrt(2x^2 + 2x + 1)  "d"x`


`int x^3tan^(-1)x  "d"x`


`int  x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))  "d"x`


`int ("d"x)/(x^3 - 1)`


`int  ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1])  "d"x`


Evaluate `int (2"e"^x + 5)/(2"e"^x + 1)  "d"x`


If `int(sin2x)/(sin5x  sin3x)dx = 1/3log|sin 3x| - 1/5log|f(x)| + c`, then f(x) = ______


Verify the following using the concept of integration as an antiderivative

`int (x^3"d"x)/(x + 1) = x - x^2/2 + x^3/3 - log|x + 1| + "C"`


Evaluate the following:

`int x^2/(1 - x^4) "d"x` put x2 = t


Evaluate the following:

`int (2x - 1)/((x - 1)(x + 2)(x - 3)) "d"x`


Evaluate the following:

`int "e"^(-3x) cos^3x  "d"x`


Evaluate the following:

`int sqrt(tanx)  "d"x`  (Hint: Put tanx = t2)


If `int "dx"/((x + 2)(x^2 + 1)) = "a"log|1 + x^2| + "b" tan^-1x + 1/5 log|x + 2| + "C"`, then ______.


`int 1/(x^2 + 1)^2 dx` = ______.


If `int dx/sqrt(16 - 9x^2)` = A sin–1 (Bx) + C then A + B = ______.


If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.


Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`


Find: `int x^4/((x - 1)(x^2 + 1))dx`.


Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.


Evaluate: 

`int 2/((1 - x)(1 + x^2))dx`


Evaluate:

`int x/((x + 2)(x - 1)^2)dx`


Evaluate.

`int (5x^2 - 6x + 3)/(2x - 3)dx`


Evaluate:

`int(2x^3 - 1)/(x^4 + x)dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×