हिंदी

Evaluate: ∫ 2 X D X - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate:  \[\int 2^x  \text{ dx }\]

योग

उत्तर

\[\int 2^x dx\]
\[ = \frac{2^x}{\ln 2} + C \left( \because \int a^x dx = \frac{a^x}{\ln a} + C \right)\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 19: Indefinite Integrals - Very Short Answers [पृष्ठ १९८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Very Short Answers | Q 46 | पृष्ठ १९८

संबंधित प्रश्न

`∫   x    \sqrt{x + 2}     dx ` 

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

` ∫ {cot x}/ { log sin x} dx `

\[\int\frac{2 \cos x - 3 \sin x}{6 \cos x + 4 \sin x} dx\]

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

\[\int\frac{10 x^9 + {10}^x \log_e 10}{{10}^x + x^{10}} dx\]

` ∫  {1+tan}/{ x + log  sec  x   dx} `

\[\int\frac{1}{\cos 3x - \cos x} dx\]

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


Evaluate the following integrals:

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

`  ∫    {1} / {cos x  + "cosec x" } dx  `

Evaluate the following integrals:

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

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

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

Evaluate the following integrals:

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

 


Evaluate the following integrals:

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

 


Evaluate the following integrals:

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

\[\int\left( x - 3 \right)\sqrt{x^2 + 3x - 18} \text{  dx }\]

Evaluate the following integral:

\[\int\frac{x^2 + 1}{\left( x^2 + 4 \right)\left( x^2 + 25 \right)}dx\]

Evaluate the following integral:

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

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

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

Write a value of

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

Evaluate:\[\int\frac{x^2}{1 + x^3} \text{ dx }\] .


Evaluate:

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

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

 


Evaluate:\[\int\frac{\sin \sqrt{x}}{\sqrt{x}} \text{ dx }\]


Evaluate:\[\int\frac{\cos \sqrt{x}}{\sqrt{x}} \text{ dx }\]


Evaluate:\[\int \sec^2 \left( 7 - 4x \right) \text{ dx }\]


Evaluate:\[\int\frac{\log x}{x} \text{ dx }\]


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


Evaluate: \[\int\left( 1 - x \right)\sqrt{x}\text{  dx }\]


Evaluate:  \[\int\frac{2}{1 - \cos2x}\text{ dx }\]


Evaluate: `int_  (x + sin x)/(1 + cos x )  dx`


Evaluate the following:

`int sqrt(1 + x^2)/x^4 "d"x`


Evaluate the following:

`int ("d"x)/sqrt(16 - 9x^2)`


Evaluate the following:

`int ("d"x)/(xsqrt(x^4 - 1))`  (Hint: Put x2 = sec θ)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×