Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\int\frac{dx}{\sqrt{3 x^2 + 5x + 7}}\]
\[ = \int\frac{dx}{\sqrt{3\left( x^2 + \frac{5}{3}x + \frac{7}{3} \right)}}\]
\[ = \frac{1}{\sqrt{3}}\int\frac{dx}{\sqrt{x^2 + \frac{5}{3}x + \left( \frac{5}{6} \right)^2 - \left( \frac{5}{6} \right)^2 + \frac{7}{3}}}\]
\[ = \frac{1}{\sqrt{3}}\int\frac{dx}{\sqrt{\left( x + \frac{5}{6} \right)^2 - \frac{25}{36} + \frac{7}{3}}}\]
\[ = \frac{1}{\sqrt{3}}\int\frac{dx}{\sqrt{\left( x + \frac{5}{6} \right)^2 + \frac{- 25 + 84}{36}}}\]
\[ = \frac{1}{\sqrt{3}}\int\frac{dx}{\sqrt{\left( x + \frac{5}{6} \right)^2 + \frac{59}{36}}}\]
\[ = \frac{1}{\sqrt{3}}\int\frac{dx}{\sqrt{\left( x + \frac{5}{6} \right)^2 + \left( \frac{\sqrt{59}}{36} \right)^2}}\]
\[ = \frac{1}{\sqrt{3}} \log \left| x + \frac{5}{6} + \sqrt{\left( x + \frac{5}{6} \right)^2 + \frac{59}{36}} \right| + C\]
\[ = \frac{1}{\sqrt{3}} \log \left| x + \frac{5}{6} + \sqrt{x^2 + \frac{5}{3}x + \frac{7}{3}} \right| + C\]
APPEARS IN
संबंधित प्रश्न
` ∫ 1 /{x^{1/3} ( x^{1/3} -1)} ` dx
\[\int\left( e^\text{log x} + \sin x \right) \text{ cos x dx }\]
Evaluate the following integral:
The primitive of the function \[f\left( x \right) = \left( 1 - \frac{1}{x^2} \right) a^{x + \frac{1}{x}} , a > 0\text{ is}\]
\[\int\sin x \sin 2x \text{ sin 3x dx }\]
\[ \int\left( 1 + x^2 \right) \ \cos 2x \ dx\]
