English

∫ ( √ X − 1 √ X ) 2 D X - Mathematics

Advertisements
Advertisements

Question

\[\int \left( \sqrt{x} - \frac{1}{\sqrt{x}} \right)^2 dx\]
Sum
Advertisements

Solution

\[\int \left( \sqrt{x} - \frac{1}{\sqrt{x}} \right)^2 dx\]
\[ = \int\left( x + \frac{1}{x} - 2 \right)dx\]
` = ∫   x dx + ∫   dx/x - 2\ ∫    x dx`
`= x^2 / 2 + In   | x|  -2 x +C`

shaalaa.com
  Is there an error in this question or solution?
Chapter 19: Indefinite Integrals - Exercise 19.02 [Page 14]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 19 Indefinite Integrals
Exercise 19.02 | Q 6 | Page 14

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

\[\int\sqrt{x}\left( x^3 - \frac{2}{x} \right) dx\]

\[\int \left( 3x + 4 \right)^2 dx\]

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

\[\int \left( a \tan x + b \cot x \right)^2 dx\]

\[\int\frac{1}{2 - 3x} + \frac{1}{\sqrt{3x - 2}} dx\]

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

\[\int\frac{x^2 + 3x - 1}{\left( x + 1 \right)^2} dx\]

\[\int \cos^2 \text{nx dx}\]

` ∫  {sin 2x} /{a cos^2  x  + b sin^2  x }  ` dx 


\[\int\left\{ 1 + \tan x \tan \left( x + \theta \right) \right\} dx\]

\[\int\frac{\sec^2 \sqrt{x}}{\sqrt{x}} dx\]

\[\int 5^{5^{5^x}} 5^{5^x} 5^x dx\]

\[\int\frac{1}{\sin^3 x \cos^5 x} dx\]

\[\int\frac{e^x}{1 + e^{2x}} dx\]

\[\int\frac{x}{x^4 + 2 x^2 + 3} dx\]

\[\int\frac{x^2}{x^6 + a^6} dx\]

\[\int\frac{1}{\sqrt{3 x^2 + 5x + 7}} dx\]

\[\int\frac{e^x}{\sqrt{16 - e^{2x}}} dx\]

\[\int\frac{x + 1}{x^2 + x + 3} dx\]

\[\int\frac{x^2 + 1}{x^2 - 5x + 6} dx\]

\[\int\frac{1}{4 \sin^2 x + 5 \cos^2 x} \text{ dx }\]

\[\int\frac{2}{2 + \sin 2x}\text{ dx }\]

\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]

\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]

\[\int x^2 \text{ cos x dx }\]

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

\[\int\left( \frac{1}{\log x} - \frac{1}{\left( \log x \right)^2} \right) dx\]

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

\[\int\left( x + 1 \right) \sqrt{2 x^2 + 3} \text{ dx}\]

\[\int\frac{x^2 + 1}{x\left( x^2 - 1 \right)} dx\]

\[\int\frac{x^2}{\left( x^2 + 1 \right) \left( 3 x^2 + 4 \right)} dx\]

\[\int\sqrt{\cot \text{θ} d  } \text{ θ}\]

\[\int\sqrt{\frac{a + x}{x}}dx\]
 

\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]

\[\int \sec^6 x\ dx\]

\[\int \tan^5 x\ \sec^3 x\ dx\]

\[\int \tan^3 x\ \sec^4 x\ dx\]

\[\int\frac{1}{\left( x^2 + 2 \right) \left( x^2 + 5 \right)} \text{ dx}\]

\[\int\frac{x^2 - 2}{x^5 - x} \text{ dx}\]

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×