Advertisements
Advertisements
प्रश्न
Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .
Advertisements
उत्तर
I = \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\]
\[I = \int\frac{dx}{\sqrt{- \left( x^2 + 2x - 3 \right)}}\]
\[ = \int\frac{dx}{\sqrt{- \left( x^2 + 2x - 4 + 1 \right)}}\]
\[ = \int\frac{dx}{\sqrt{- \left[ \left( x^2 + 2x + 1 \right) - 2^2 \right]}}\]
\[= \int\frac{dx}{\sqrt{- \left[ \left( x + 1 \right)^2 - 2^2 \right]}}\]
\[ = \int\frac{dx}{\sqrt{2^2 - \left( x + 1 \right)^2}}\]
\[ = \sin^{- 1} \left( \frac{x + 1}{2} \right) + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( \frac{m}{x} + \frac{x}{m} + m^x + x^m + mx \right) dx\]
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
\[\int\frac{\sin^3 x - \cos^3 x}{\sin^2 x \cos^2 x} dx\]
` ∫ cos 3x cos 4x` dx
\[\int\frac{1 - \sin 2x}{x + \cos^2 x} dx\]
\[\int\frac{1}{\left( x + 1 \right)\left( x^2 + 2x + 2 \right)} dx\]
\[\int \cot^6 x \text{ dx }\]
\[\int \sin^5 x \text{ dx }\]
\[\int\frac{1}{x^2 + 6x + 13} dx\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]
\[\int\frac{1}{1 - \cot x} dx\]
\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]
\[\int x^2 \cos 2x\ \text{ dx }\]
\[\int x^2 \text{ cos x dx }\]
\[\int x \sin x \cos 2x\ dx\]
\[\int\frac{x^2 \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx }\]
\[\int\frac{5x}{\left( x + 1 \right) \left( x^2 - 4 \right)} dx\]
\[\int\frac{x^3}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{3x + 5}{x^3 - x^2 - x + 1} dx\]
\[\int\frac{\left( x^2 + 1 \right) \left( x^2 + 2 \right)}{\left( x^2 + 3 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{x^2 + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{1}{x^4 + 3 x^2 + 1} \text{ dx }\]
\[\int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int \tan^4 x\ dx\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\sqrt{\frac{a + x}{x}}dx\]
\[\int\frac{\sin^6 x}{\cos x} \text{ dx }\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int\frac{\sin x + \cos x}{\sin^4 x + \cos^4 x} \text{ dx }\]
