Advertisements
Advertisements
प्रश्न
\[\int\frac{\cos\sqrt{x}}{\sqrt{x}} dx\]
योग
Advertisements
उत्तर
\[\int\frac{\cos \sqrt{x}}{\sqrt{x}}dx\]
\[\text{Let} \sqrt{x} = t\]
\[ \Rightarrow \frac{1}{2\sqrt{x}} = \frac{dt}{dx}\]
\[ \Rightarrow \frac{dx}{\sqrt{x}} = 2 dt\]
\[Now, \int\frac{\cos \sqrt{x}}{\sqrt{x}}dx\]
\[ = 2\int\text{cos t dt} \]
\[ = 2 \sin t + C\]
\[ = 2 \sin \sqrt{x} + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int \left( 3x + 4 \right)^2 dx\]
` ∫ {cosec x} / {"cosec x "- cot x} ` dx
\[\int \cot^{- 1} \left( \frac{\sin 2x}{1 - \cos 2x} \right) dx\]
Write the primitive or anti-derivative of
\[f\left( x \right) = \sqrt{x} + \frac{1}{\sqrt{x}} .\]
\[\int\frac{1 + \cos 4x}{\cot x - \tan x} dx\]
\[\int\frac{\text{sin} \left( x - \alpha \right)}{\text{sin }\left( x + \alpha \right)} dx\]
\[\int\frac{e^x + 1}{e^x + x} dx\]
\[\int\frac{1 - \sin x}{x + \cos x} dx\]
\[\int\frac{1}{ x \text{log x } \text{log }\left( \text{log x }\right)} dx\]
\[\int\frac{\sin 2x}{\sin 5x \sin 3x} dx\]
\[\int 5^{5^{5^x}} 5^{5^x} 5^x dx\]
\[\int \sin^5 x \text{ dx }\]
\[\int\frac{\sec^2 x}{1 - \tan^2 x} dx\]
\[\int\frac{e^x}{1 + e^{2x}} dx\]
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
\[\int\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{1}{\sin x + \sqrt{3} \cos x} \text{ dx }\]
\[\int2 x^3 e^{x^2} dx\]
\[\int x^3 \cos x^2 dx\]
\[\int e^x \sec x \left( 1 + \tan x \right) dx\]
\[\int\sqrt{3 - 2x - 2 x^2} \text{ dx}\]
\[\int\sqrt{2ax - x^2} \text{ dx}\]
\[\int\frac{1}{x \log x \left( 2 + \log x \right)} dx\]
\[\int\frac{1}{\left( x - 1 \right) \left( x + 1 \right) \left( x + 2 \right)} dx\]
\[\int\frac{x}{\left( x - 1 \right)^2 \left( x + 2 \right)} dx\]
\[\int\frac{3x + 5}{x^3 - x^2 - x + 1} dx\]
Find \[\int\frac{2x}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)^2}dx\]
\[\int\frac{x^2 + 9}{x^4 + 81} \text{ dx }\]
\[\int\frac{x^2 + 1}{x^4 + 7 x^2 + 1} 2 \text{ dx }\]
\[\int\frac{x}{\left( x - 3 \right) \sqrt{x + 1}} \text{ dx}\]
The value of \[\int\frac{\sin x + \cos x}{\sqrt{1 - \sin 2x}} dx\] is equal to
\[\int\frac{\sin x}{\cos 2x} \text{ dx }\]
\[\int \cot^4 x\ dx\]
\[\int\frac{1}{\sin^4 x + \cos^4 x} \text{ dx}\]
\[\int \tan^5 x\ \sec^3 x\ dx\]
\[ \int\left( 1 + x^2 \right) \ \cos 2x \ dx\]
\[\int x \sec^2 2x\ dx\]
\[\int x^3 \left( \log x \right)^2\text{ dx }\]
\[\int\frac{1}{1 + x + x^2 + x^3} \text{ dx }\]
\[\int\frac{\cos^7 x}{\sin x} dx\]
