हिंदी

∫ 5 X 4 + 12 X 3 + 7 X 2 X 2 + X D X - Mathematics

Advertisements
Advertisements

प्रश्न

\[\int\frac{5 x^4 + 12 x^3 + 7 x^2}{x^2 + x} dx\]

योग
Advertisements

उत्तर

\[\int\left( \frac{5 x^4 + 12 x^3 + 7 x^2}{x^2 + x} \right)dx\]

\[ = \int \frac{x^2 \left( 5 x^2 + 12x + 7 \right)}{x\left( x + 1 \right)}dx\]

 `= ∫ x {( 5 x^2 + 5x + 7x + 7 )}/{( x + 1 )}`

\[ = \int\frac{x\left( 5x\left( x + 1 \right) + 7\left( x + 1 \right) \right)}{\left( x + 1 \right)}dx\]

` = ∫ x{ ( 5x + 7 )( x + 1 )}/{( x + 1 )}dx`

\[ = \int\left( 5 x^2 + 7x \right)dx\]

\[ = \frac{5 x^3}{3} + \frac{7 x^2}{2} + C\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 19: Indefinite Integrals - Exercise 19.02 [पृष्ठ १५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Exercise 19.02 | Q 20 | पृष्ठ १५

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

\[\int\left( 3x\sqrt{x} + 4\sqrt{x} + 5 \right)dx\]

\[\int\frac{5 \cos^3 x + 6 \sin^3 x}{2 \sin^2 x \cos^2 x} dx\]

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

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

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


` ∫  tan 2x tan 3x  tan 5x    dx  `

`  =  ∫ root (3){ cos^2 x}  sin x   dx `


\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]

\[\int\frac{\cos\sqrt{x}}{\sqrt{x}} dx\]

\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]

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

 ` ∫   1 /{x^{1/3} ( x^{1/3} -1)}   ` dx


\[\int \sin^4 x \cos^3 x \text{ dx }\]

\[\int \sin^7 x  \text{ dx }\]

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

\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]

\[\int\frac{1 - 3x}{3 x^2 + 4x + 2}\text{  dx}\]

\[\int\frac{x^3}{x^4 + x^2 + 1}dx\]

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

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

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

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

\[\int e^x \left( \tan x - \log \cos x \right) dx\]

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

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

\[\int\frac{1}{x^4 + 3 x^2 + 1} \text{ dx }\]

` \int \text{ x} \text{ sec x}^2 \text{  dx  is  equal  to }`

 


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

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

\[\int\frac{\cos x}{\frac{1}{4} - \cos^2 x} \text{ dx }\]

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


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

\[\int \log_{10} x\ dx\]

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

Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×