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

Evaluate the following integrals: ∫xx+2.dx

Advertisements
Advertisements

प्रश्न

Evaluate the following integrals:

`int x/(x + 2).dx`

बेरीज
Advertisements

उत्तर

`int x/(x + 2).dx`

= `int((x + 2) - 2)/(x + 2).dx`

= `int ((x + 2)/(x + 2) - 2/(x + 2)).dx`

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

= x – 2 log |x + 2| + c.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Indefinite Integration - Exercise 3.1 [पृष्ठ १०२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Indefinite Integration
Exercise 3.1 | Q 3.01 | पृष्ठ १०२

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:


Evaluate : `∫1/(3+2sinx+cosx)dx`


Evaluate `int 1/(3+ 2 sinx + cosx) dx`


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

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]

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


Write a value of

\[\int\frac{1 + \log x}{3 + x \log x} \text{ dx }\] .

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


\[If \int e^x \left( \tan x + 1 \right)\text{ sec  x  dx } = e^x f\left( x \right) + C, \text{ then  write  the value  of  f}\left( x \right) .\]

 

 


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


Evaluate the following integrals : `int sin x/cos^2x dx`


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


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


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


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


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


Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`


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


Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`


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


Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`


Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`


Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`


Evaluate the following.

`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx


Evaluate `int "x - 1"/sqrt("x + 4")` dx


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


Evaluate: `int "e"^sqrt"x"` dx


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


`int 1/sqrt((x - 3)(x + 2))` dx = ______.


`int 1/(cos x - sin x)` dx = _______________


`int (log x)/(log ex)^2` dx = _________


State whether the following statement is True or False:

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`


General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)


`int (f^'(x))/(f(x))dx` = ______ + c.


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


`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`


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


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


`int "cosec"^4x  dx` = ______.


`int 1/(sin^2x cos^2x)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:

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


Evaluate the following

`int x^3 e^(x^2) ` dx


Evaluate the following.

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


Evaluate the following.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×