मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

To find the value of ∫(1+logx)x dx the proper substitution is ______ - Mathematics and Statistics

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प्रश्न

To find the value of `int ((1 + logx))/x` dx the proper substitution is ______

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उत्तर

1 + log x = t

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पाठ 1.5: Integration - Q.2

संबंधित प्रश्‍न

Evaluate : `int(x-3)sqrt(x^2+3x-18)  dx`


Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Integrate the functions:

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


Integrate the functions:

`(e^(2x) -  e^(-2x))/(e^(2x) + e^(-2x))`


Integrate the functions:

`cos sqrt(x)/sqrtx`


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


Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].


Evaluate the following integrals:

`int (sin4x)/(cos2x).dx`


Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`


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

x9.sec2(x10)


Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`


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


Integrate the following functions w.r.t. x : tan5x


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


Evaluate the following : `(1)/(4x^2 - 20x + 17)`


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


Evaluate the following.

∫ (x + 1)(x + 2)7 (x + 3)dx


Evaluate the following.

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


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


`int logx/x  "d"x`


If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 


`int x/sqrt(1 - 2x^4) dx` = ______.

(where c is a constant of integration)


Write `int cotx  dx`.


Evaluate the following.

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


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate the following.

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


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


Evaluate `int1/(x(x-1))dx` 


Evaluate the following:

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


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