Advertisements
Advertisements
प्रश्न
\[\int\frac{1}{x^2 - 10x + 34} dx\]
बेरीज
Advertisements
उत्तर
\[\int\frac{dx}{x^2 - 10x + 34}\]
\[ = \int\frac{dx}{x^2 - 10x + 25 - 25 + 34}\]
\[ = \int\frac{dx}{\left( x - 5 \right)^2 + 9}\]
\[ = \int\frac{dx}{\left( x - 5 \right)^2 + 3^2}\]
\[\text{ let x } - 5 = t\]
\[ \Rightarrow dx = dt\]
\[Now, \int\frac{dx}{\left( x - 5 \right)^2 + 3^2}\]
\[ = \int\frac{dt}{t^2 + 3^2}\]
\[ = \frac{1}{3} \tan^{- 1} \left( \frac{t}{3} \right) + C\]
\[ = \frac{1}{3} \tan^{- 1} \left( \frac{x - 5}{3} \right) + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{1}{\text{cos}^2\text{ x }\left( 1 - \text{tan x} \right)^2} dx\]
\[\int\frac{x^3}{x - 2} dx\]
\[\int\frac{3x + 5}{\sqrt{7x + 9}} dx\]
\[\int\frac{1 - \sin 2x}{x + \cos^2 x} dx\]
\[\int\frac{\left( 1 + \sqrt{x} \right)^2}{\sqrt{x}} dx\]
` ∫ e^{m sin ^-1 x}/ \sqrt{1-x^2} ` dx
\[\int\frac{x^2}{\sqrt{3x + 4}} dx\]
\[\int\frac{x^2 + 3x + 1}{\left( x + 1 \right)^2} dx\]
\[\int\frac{1}{a^2 - b^2 x^2} dx\]
\[\int\frac{1}{\sqrt{7 - 3x - 2 x^2}} dx\]
\[\int\frac{\cos 2x}{\sqrt{\sin^2 2x + 8}} dx\]
\[\int\frac{1 - 3x}{3 x^2 + 4x + 2}\text{ dx}\]
\[\int\frac{5x + 3}{\sqrt{x^2 + 4x + 10}} \text{ dx }\]
\[\int\frac{\cos x}{\cos 3x} \text{ dx }\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
\[\int\frac{1}{4 \cos x - 1} \text{ dx }\]
\[\int x e^x \text{ dx }\]
\[\int2 x^3 e^{x^2} dx\]
\[\int\cos\sqrt{x}\ dx\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx }\]
\[\int x^2 \sin^{- 1} x\ dx\]
\[\int\left( x + 1 \right) \text{ log x dx }\]
\[\int e^x \frac{x - 1}{\left( x + 1 \right)^3} \text{ dx }\]
\[\int\frac{e^x \left( x - 4 \right)}{\left( x - 2 \right)^3} \text{ dx }\]
\[\int\frac{2x - 3}{\left( x^2 - 1 \right) \left( 2x + 3 \right)} dx\]
\[\int\frac{5 x^2 + 20x + 6}{x^3 + 2 x^2 + x} dx\]
\[\int\frac{3}{\left( 1 - x \right) \left( 1 + x^2 \right)} dx\]
\[\int\frac{4 x^4 + 3}{\left( x^2 + 2 \right) \left( x^2 + 3 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{x^2 + 9}{x^4 + 81} \text{ dx }\]
\[\int\frac{1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\left( x - 1 \right) e^{- x} dx\] is equal to
\[\int \sec^2 x \cos^2 2x \text{ dx }\]
\[\int \cot^5 x\ dx\]
\[\int\sqrt{\sin x} \cos^3 x\ \text{ dx }\]
\[\int\frac{\sin x}{\sqrt{\cos^2 x - 2 \cos x - 3}} \text{ dx }\]
\[\int\sqrt{\frac{a + x}{x}}dx\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int x^2 \tan^{- 1} x\ dx\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
