Advertisements
Advertisements
प्रश्न
\[\int\frac{1 - \cot x}{1 + \cot x} dx\]
बेरीज
Advertisements
उत्तर
\[\text{Let I} = \int\left( \frac{1 - \cot x}{1 + \cot x} \right)dx\]
\[ = \int\left( \frac{1 - \frac{\cos x}{\sin x}}{1 + \frac{\cos x}{\sin x}} \right)dx\]
\[ = \int\left( \frac{\sin x - \cos x}{\sin x + \cos x} \right)dx\]
\[\text{Putting }\sin x + \cos x = t\]
\[ \Rightarrow \left( \cos x - \sin x \right)dx = dt\]
\[ \Rightarrow \left( \sin x - \cos x \right)dx = - dt\]
\[ \therefore I = \int\frac{- dt}{t}\]
\[ = - \text{ln }\left| t \right| + C\]
\[ = - \text{ln} \left| \sin x + \cos x \right| + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( 2^x + \frac{5}{x} - \frac{1}{x^{1/3}} \right)dx\]
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
If f' (x) = x − \[\frac{1}{x^2}\] and f (1) \[\frac{1}{2}, find f(x)\]
\[\int\frac{1}{\sqrt{x + 1} + \sqrt{x}} dx\]
\[\int\frac{1}{x (3 + \log x)} dx\]
\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]
\[\int\frac{\cos^5 x}{\sin x} dx\]
\[\int\frac{e^{m \tan^{- 1} x}}{1 + x^2} dx\]
\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[\int\frac{x^5}{\sqrt{1 + x^3}} dx\]
` ∫ sec^6 x tan x dx `
\[\int \sin^5 x \cos x \text{ dx }\]
\[\int\frac{1}{x^2 - 10x + 34} dx\]
\[\int\frac{e^x}{1 + e^{2x}} dx\]
\[\int\frac{x^2}{x^6 + a^6} dx\]
\[\int\frac{x}{x^2 + 3x + 2} dx\]
\[\int\frac{2x - 3}{x^2 + 6x + 13} dx\]
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
`int"x"^"n"."log" "x" "dx"`
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx }\]
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int\left( x + 1 \right) \sqrt{2 x^2 + 3} \text{ dx}\]
\[\int\frac{1}{\sin x \left( 3 + 2 \cos x \right)} dx\]
\[\int\frac{\left( x - 1 \right)^2}{x^4 + x^2 + 1} \text{ dx}\]
\[\int\frac{1}{\left( 1 + x^2 \right) \sqrt{1 - x^2}} \text{ dx }\]
\[\int\frac{x}{4 + x^4} \text{ dx }\] is equal to
\[\int \cot^5 x\ dx\]
\[\int x\sqrt{2x + 3} \text{ dx }\]
\[\int\frac{1}{4 x^2 + 4x + 5} dx\]
\[\int\frac{1}{\sin x \left( 2 + 3 \cos x \right)} \text{ dx }\]
\[\int \sec^4 x\ dx\]
\[\int\frac{\log \left( 1 - x \right)}{x^2} \text{ dx}\]
\[\int\frac{1}{x \sqrt{1 + x^n}} \text{ dx}\]
\[\int\frac{1 + x^2}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int\frac{x}{x^3 - 1} \text{ dx}\]
\[\int\frac{x^2 - 2}{x^5 - x} \text{ dx}\]
\[\int \sin^3 \left( 2x + 1 \right) \text{dx}\]
\[\int\frac{\cos^7 x}{\sin x} dx\]
