Advertisements
Advertisements
प्रश्न
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
बेरीज
Advertisements
उत्तर
\[\int\left[ \frac{2x - 1}{\left( x - 1 \right)^2} \right]dx\]
\[ = \int\left[ \frac{2x - 2 + 2 - 1}{\left( x - 1 \right)^2} \right]dx\]
\[ = \int\left( \frac{2 \left( x - 1 \right)}{\left( x - 1 \right)^2} + \frac{1}{\left( x - 1 \right)^2} \right)dx\]
\[ = 2\int\frac{dx}{x - 1} + \int \left( x - 1 \right)^{- 2} dx\]
\[ = \text{2 ln }\left| x - 1 \right| + \frac{\left( x - 1 \right)^{- 2 + 1}}{- 2 + 1} + C\]
\[ = \text{2 ln }\left| x - 1 \right| - \frac{1}{x - 1} + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
\[\int\sqrt{x}\left( x^3 - \frac{2}{x} \right) dx\]
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
\[\int \tan^2 \left( 2x - 3 \right) dx\]
` ∫ {"cosec" x }/ { log tan x/2 ` dx
\[\int \sin^5\text{ x }\text{cos x dx}\]
\[\int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2} dx\]
\[\int\frac{x + \sqrt{x + 1}}{x + 2} dx\]
\[\int\frac{x^2 + 3x + 1}{\left( x + 1 \right)^2} dx\]
\[\int \sin^4 x \cos^3 x \text{ dx }\]
\[\int \sin^3 x \cos^6 x \text{ dx }\]
\[\int\frac{1}{a^2 - b^2 x^2} dx\]
\[\int\frac{\cos x}{\sin^2 x + 4 \sin x + 5} dx\]
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
\[\int\frac{\left( 3\sin x - 2 \right)\cos x}{13 - \cos^2 x - 7\sin x}dx\]
\[\int\frac{x^2 + 1}{x^2 - 5x + 6} dx\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int\frac{1}{4 \cos x - 1} \text{ dx }\]
\[\int\frac{1}{13 + 3 \cos x + 4 \sin x} dx\]
\[\int\frac{1}{\sin x + \sqrt{3} \cos x} \text{ dx }\]
\[\int\frac{1}{\sqrt{3} \sin x + \cos x} dx\]
\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]
\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]
`int"x"^"n"."log" "x" "dx"`
\[\int\frac{x^2 \tan^{- 1} x}{1 + x^2} \text{ dx }\]
\[\int\left( \tan^{- 1} x^2 \right) x\ dx\]
\[\int\sqrt{2ax - x^2} \text{ dx}\]
\[\int\frac{3 + 4x - x^2}{\left( x + 2 \right) \left( x - 1 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{3x + 5}{x^3 - x^2 - x + 1} dx\]
\[\int\frac{x}{\left( x^2 + 4 \right) \sqrt{x^2 + 9}} \text{ dx}\]
\[\int\frac{1}{1 - \cos x - \sin x} dx =\]
\[\int\frac{1}{\sqrt{x} + \sqrt{x + 1}} \text{ dx }\]
\[\int\frac{1}{e^x + 1} \text{ dx }\]
\[\int\frac{1}{e^x + e^{- x}} dx\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int \left( e^x + 1 \right)^2 e^x dx\]
Find: `int (3x +5)/(x^2+3x-18)dx.`
