मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

If ∫1x+x5 dx = f(x) + c, then ∫x4x+x5dx = ______

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प्रश्न

If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______

पर्याय

  • f(x) − log x + c

  • f(x) + log x + c

  • log x − f(x) + c

  • `1/5x^5` f(x) + c

MCQ
रिकाम्या जागा भरा
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उत्तर

log x − f(x) + c

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पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Evaluate: `int sqrt(tanx)/(sinxcosx) dx`


Integrate the functions:

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


Integrate the functions:

`xsqrt(x + 2)`


Integrate the functions:

(4x + 2) `sqrt(x^2 + x +1)`


Integrate the functions:

`x^2/(2+ 3x^3)^3`


Integrate the functions:

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


\[\int\sqrt{x^2 + x + 1} \text{ dx}\]

Evaluate the following integrals:

tan2x dx


Integrate the following functions w.r.t. x : `(logx)^n/x`


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

x9.sec2(x10)


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


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

`(1)/(sinx.cosx + 2cos^2x)`


Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`


Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`


Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`


Evaluate the following : `int  (1)/(x^2 + 8x + 12).dx`


Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`


Evaluate the following integrals:

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


Choose the correct options from the given alternatives :

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


Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx


If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).


Evaluate the following.

`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx


Evaluate the following.

`int 1/(4x^2 - 20x + 17)` dx


Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx


Evaluate the following.

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


Choose the correct alternative from the following.

`int "dx"/(("x" - "x"^2))`= 


Evaluate `int 1/((2"x" + 3))` dx


Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).


Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx


`int 2/(sqrtx - sqrt(x + 3))` dx = ________________


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


`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


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


Evaluate the following.

`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`


if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`


If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)


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


Solve the following Evaluate.

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


Evaluate:

`int 1/(1 + cosα . cosx)dx`


`int "cosec"^4x  dx` = ______.


Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`


The value of `int ("d"x)/(sqrt(1 - x))` is ______.


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


Evaluate the following.

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


If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Which substitution is appropriate for \[\sqrt{\frac{x}{x-a}}\], \[\sqrt{\frac{x-a}{x}}\], \[\sqrt{x(x-\mathrm{a})}\], or \[\frac{1}{\sqrt{x(x-\mathrm{a})}}\]?


For indefinite integrals, what should be done after integration in the new variable?


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