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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

∫x21-x6 dx = ________________

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प्रश्न

`int x^2/sqrt(1 - x^6)` dx = ________________

पर्याय

  • −sin−1 (x3) + c

  • cos−1 (x3) + c

  • sin−1 (x3) + c

  • `1/3 sin^(-1) (x^3) + "c"`

MCQ
रिकाम्या जागा भरा
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उत्तर

`1/3 sin^(-1) (x^3) + "c"`

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पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Integrate the functions:

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


Integrate the functions:

`cos sqrt(x)/sqrtx`


Integrate the functions:

`sin x/(1+ cos x)`


Integrate the functions:

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


Evaluate: `int 1/(x(x-1)) dx`


Evaluate: `int (2y^2)/(y^2 + 4)dx`


\[\int\sqrt{3 + 2x - x^2} \text{ dx}\]

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].


Write a value of\[\int a^x e^x \text{ dx }\]


Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]


 Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log  |"x" +sqrt("x"^2 +"a"^2) | + "c"`


Integrate the following w.r.t. x : x3 + x2 – x + 1


Evaluate the following integral: 

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


Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`


Integrate the following function w.r.t. x:

x9.sec2(x10)


Integrate the following functions w.r.t. x : `cosx/sin(x - a)`


Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`


Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`


Evaluate the following integrals:

`int (2x + 1)/(x^2 + 4x - 5).dx`


Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


Integrate the following with respect to the respective variable:

`x^7/(x + 1)`


Evaluate the following.

`int "x" sqrt(1 + "x"^2)` dx


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx


Choose the correct alternative from the following.

`int "x"^2 (3)^("x"^3) "dx"` =


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


Fill in the Blank.

`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


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


Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx


`int cos^7 x  "d"x`


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


If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.


`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.


`int (sin  (5x)/2)/(sin  x/2)dx` is equal to ______. (where C is a constant of integration).


The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.


`int (x + sinx)/(1 + cosx)dx` is equal to ______.


Find `int dx/sqrt(sin^3x cos(x - α))`.


`int secx/(secx - tanx)dx` equals ______.


Evaluate `int(1+ x + x^2/(2!)) dx`


Evaluate `int(1 + x + x^2/(2!))dx`


Evaluate `int1/(x(x - 1))dx`


Evaluate:

`int sin^2(x/2)dx`


Evaluate the following.

`int1/(x^2+4x-5)dx`


Evaluate the following.

`intx^3/sqrt(1 + x^4)dx`


Evaluate the following:

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


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