Advertisements
Advertisements
प्रश्न
\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
बेरीज
Advertisements
उत्तर
\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[\text{Let 2 + 3 }\log x = t\]
\[ \Rightarrow \frac{3}{x} = \frac{dt}{dx}\]
\[ \Rightarrow \frac{dx}{x} = \frac{dt}{3}\]
Now, \[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[ = \frac{1}{3}\int \text{sin t dt}\]
\[ = \frac{1}{3} \left[ - \text{cos t }\right] + C\]
\[ = - \frac{1}{3}\text{cos }\left( \text{2 + 3 log x }\right) + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( \sec^2 x + {cosec}^2 x \right) dx\]
\[\int\frac{\left( x^3 + 8 \right)\left( x - 1 \right)}{x^2 - 2x + 4} dx\]
\[\int\frac{x^3 - 3 x^2 + 5x - 7 + x^2 a^x}{2 x^2} dx\]
\[\int\frac{1}{\sqrt{2x + 3} + \sqrt{2x - 3}} dx\]
\[\int \sin^2\text{ b x dx}\]
\[\int\frac{x + 1}{x \left( x + \log x \right)} dx\]
\[\int\frac{\sin 2x}{\sin \left( x - \frac{\pi}{6} \right) \sin \left( x + \frac{\pi}{6} \right)} dx\]
\[\int\frac{1}{1 + \sqrt{x}} dx\]
\[\int\frac{x^5}{\sqrt{1 + x^3}} dx\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
\[\int\frac{x^2}{\sqrt{1 - x}} dx\]
` ∫ tan x sec^4 x dx `
` ∫ tan^5 x sec ^4 x dx `
` = ∫1/{sin^3 x cos^ 2x} dx`
\[\int\frac{1}{x^2 - 10x + 34} dx\]
\[\int\frac{1}{x\sqrt{4 - 9 \left( \log x \right)^2}} dx\]
\[\int\frac{\cos x}{\sqrt{\sin^2 x - 2 \sin x - 3}} dx\]
\[\int\frac{x + 2}{2 x^2 + 6x + 5}\text{ dx }\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{\cos x}{\cos 3x} \text{ dx }\]
\[\int x^3 \text{ log x dx }\]
\[\int\left( x + 1 \right) \text{ e}^x \text{ log } \left( x e^x \right) dx\]
\[\int\frac{e^x \left( x - 4 \right)}{\left( x - 2 \right)^3} \text{ dx }\]
\[\int\frac{\sqrt{16 + \left( \log x \right)^2}}{x} \text{ dx}\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{\cos x}{\left( 1 - \sin x \right)^3 \left( 2 + \sin x \right)} dx\]
\[\int\frac{1}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)} dx\]
\[\int\frac{1}{x \left( x^4 - 1 \right)} dx\]
\[\int\frac{x^2 + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{x^2 - 1}{x^4 + 1} \text{ dx }\]
\[\int\frac{x}{\left( x - 3 \right) \sqrt{x + 1}} dx\]
\[\int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\} dx =\]
\[\int \cos^3 (3x)\ dx\]
\[\int\frac{1}{e^x + 1} \text{ dx }\]
\[\int \tan^3 x\ dx\]
\[\int x\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{x \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx}\]
\[\int\frac{x}{x^3 - 1} \text{ dx}\]
\[\int\frac{x^2 - 2}{x^5 - x} \text{ dx}\]
