हिंदी

Evaluate: ∫ E Log √ X X D X

Advertisements
Advertisements

प्रश्न

Evaluate:

\[\int\frac{e\log \sqrt{x}}{x}dx\]
योग
Advertisements

उत्तर

\[\int\frac{e\log\sqrt{x}}{x}dx\]
\[ = \int\frac{\sqrt{x}}{x}dx\]
\[ = \int\frac{1}{\sqrt{x}} dx\]
\[ = \int x^{- \frac{1}{2}} dx\]
\[ = \left[ \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} \right] + C\]
\[ = 2\sqrt{x} + C\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 18: Indefinite Integrals - Exercise 19.01 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 18 Indefinite Integrals
Exercise 19.01 | Q 6 | पृष्ठ ४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate : `int1/(3+5cosx)dx`


 

find `∫_2^4 x/(x^2 + 1)dx`

 

Evaluate :

`∫_0^π(4x sin x)/(1+cos^2 x) dx`


Evaluate: `intsinsqrtx/sqrtxdx`

 


Evaluate the integral by using substitution.

`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`


Evaluate the integral by using substitution.

`int_0^2 xsqrt(x+2)`  (Put x + 2 = `t^2`)


Evaluate the integral by using substitution.

`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`


The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.


`int 1/(1 + cos x)` dx = _____

A) `tan(x/2) + c`

B) `2 tan (x/2) + c`

C) -`cot (x/2) + c`

D) -2 `cot (x/2)` + c


Evaluate of the following integral:

\[\int 3^{2 \log_3} {}^x dx\]

Evaluate:

\[\int\sqrt{\frac{1 - \cos 2x}{2}}dx\]

Evaluate : 

\[\int\frac{e^{6 \log_e x} - e^{5 \log_e x}}{e^{4 \log_e x} - e^{3 \log_e x}}dx\]

Evaluate the following integral:

\[\int\limits_0^3 \left| 3x - 1 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_1^2 \left| x - 3 \right| dx\]

Evaluate the following integral:

\[\int\limits_0^{2\pi} \left| \sin x \right| dx\]

 


Evaluate the following integral:

\[\int\limits_{- \pi/2}^{\pi/2} \left\{ \sin \left| x \right| + \cos \left| x \right| \right\} dx\]

 


Evaluate each of the following integral:

\[\int_0^{2\pi} \frac{e^\ sin x}{e^\ sin x + e^{- \ sin x}}dx\]

 


Evaluate each of the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}}dx\]

 


Evaluate each of the following integral:

\[\int_{- \frac{\pi}{2}}^\frac{\pi}{2} \frac{\cos^2 x}{1 + e^x}dx\]

Evaluate the following integral:

\[\int_0^\pi x\sin x \cos^2 xdx\]

Evaluate the following integral:

\[\int_{- 2}^2 \frac{3 x^3 + 2\left| x \right| + 1}{x^2 + \left| x \right| + 1}dx\]

Evaluate the following integral:

\[\int_0^\pi \left( \frac{x}{1 + \sin^2 x} + \cos^7 x \right)dx\]

Evaluate 

\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]


Evaluate the following integral:

\[\int_0^\frac{\pi}{2} \frac{a\sin x + b\sin x}{\sin x + \cos x}dx\]

 


Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .


Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .


Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .


Evaluate: `int_  e^x ((2+sin2x))/cos^2 x dx`


Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.


`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.


Find: `int (dx)/sqrt(3 - 2x - x^2)`


`int_0^1 x^2e^x dx` = ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×