हिंदी

∫ X + 5 3 X 2 + 13 X − 10 D X - Mathematics

Advertisements
Advertisements

प्रश्न

\[\int\frac{x + 5}{3 x^2 + 13x - 10}\text{ dx }\]
योग
Advertisements

उत्तर

\[I = \int\frac{x + 5}{3 x^2 + 13x - 10}dx\]
\[ = \int\frac{x + 5}{3 x^2 + 15x - 2x - 10}dx\]
\[ = \int\frac{x + 5}{3x\left( x + 5 \right) - 2\left( x + 5 \right)}dx\]
\[ = \int\frac{x + 5}{\left( 3x - 2 \right)\left( x + 5 \right)}dx\]

\[= \int\frac{x + 5}{(3x - 2)(x + 5)}dx\]
\[ = \int\frac{1}{3x - 2}dx\]
\[ \therefore I = \frac{1}{3}\text{ ln }\left| 3x - 2 \right| + c\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 19: Indefinite Integrals - Exercise 19.19 [पृष्ठ १०४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Exercise 19.19 | Q 13 | पृष्ठ १०४

संबंधित प्रश्न

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


`∫   x    \sqrt{x + 2}     dx ` 

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

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

\[\int\frac{1}{x \log x} dx\]

` ∫ {cot x}/ { log sin x} dx `

\[\int\frac{1}{\cos\left( x + a \right) \cos\left( x + b \right)}dx\]

\[\int\frac{sec x}{\log \left( \text{sec x }+ \text{tan x} \right)} dx\]

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

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

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

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


Evaluate the following integrals:

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

Evaluate the following integrals:

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

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

Evaluate the following integrals:

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

 


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

Evaluate the following integral :-

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

\[\int\frac{a x^2 + bx + c}{\left( x - a \right) \left( x - b \right) \left( x - c \right)} dx,\text{ where a, b, c are distinct}\]

Evaluate the following integral:

\[\int\frac{x^2}{\left( x^2 + 4 \right)\left( x^2 + 9 \right)}dx\]

Evaluate the following integral:

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

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

Evaluate the following integrals:

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

Evaluate the following integral:

\[\int\frac{x^2}{x^4 - x^2 - 12}dx\]

 


\[\int\frac{( x^2 + 1) ( x^2 + 4)}{( x^2 + 3) ( x^2 - 5)} dx\]

Write a value of

\[\int\frac{\log x^n}{x} \text{ dx}\]

Evaluate:

\[\int\frac{x^2 + 4x}{x^3 + 6 x^2 + 5} \text{ dx }\]

Evaluate:  \[\int 2^x  \text{ dx }\]


Evaluate:\[\int\frac{e\tan^{- 1} x}{1 + x^2} \text{ dx }\]


Evaluate: \[\int\frac{1}{x^2 + 16}\text{ dx }\]


Evaluate:

`∫ (1)/(sin^2 x cos^2 x) dx`


Evaluate the following:

`int (3x - 1)/sqrt(x^2 + 9) "d"x`


Evaluate the following:

`int sqrt(2"a"x - x^2)  "d"x`


Evaluate the following:

`int_1^2 ("d"x)/sqrt((x - 1)(2 - x))`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×