Advertisements
Advertisements
प्रश्न
\[\int\frac{1}{\sqrt{a^2 - b^2 x^2}} dx\]
योग
Advertisements
उत्तर
\[\int\frac{dx}{\sqrt{a^2 - b^2 x^2}}\]
\[ = \int\frac{dx}{\sqrt{b^2 \left( \frac{a^2}{b^2} - x^2 \right)}}\]
\[ = \frac{1}{b}\int\frac{dx}{\sqrt{\left( \frac{a}{b} \right)^2 - x^2}}\]
\[ = \frac{1}{b} \sin^{- 1} \left( \frac{xb}{a} \right) + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
`int{sqrtx(ax^2+bx+c)}dx`
\[\int\sqrt{x}\left( 3 - 5x \right) dx\]
\[\int \left( a \tan x + b \cot x \right)^2 dx\]
\[\int\sin x\sqrt{1 + \cos 2x} dx\]
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
\[\int\frac{3x + 5}{\sqrt{7x + 9}} dx\]
` ∫ cos mx cos nx dx `
\[\int\frac{\text{sin} \left( x - a \right)}{\text{sin}\left( x - b \right)} dx\]
` ∫ {sec x "cosec " x}/{log ( tan x) }` dx
\[\int\frac{1}{ x \text{log x } \text{log }\left( \text{log x }\right)} dx\]
\[\int\frac{1 + \cot x}{x + \log \sin x} dx\]
\[\int\frac{e^\sqrt{x} \cos \left( e^\sqrt{x} \right)}{\sqrt{x}} dx\]
\[\int 5^{x + \tan^{- 1} x} . \left( \frac{x^2 + 2}{x^2 + 1} \right) dx\]
\[\int\frac{1}{\left( x + 1 \right)\left( x^2 + 2x + 2 \right)} dx\]
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
Evaluate the following integrals:
\[\int\cos\left\{ 2 \cot^{- 1} \sqrt{\frac{1 + x}{1 - x}} \right\}dx\]
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]
\[\int\frac{\sin x - \cos x}{\sqrt{\sin 2x}} dx\]
`int"x"^"n"."log" "x" "dx"`
\[\int\frac{\log x}{x^n}\text{ dx }\]
\[\int\frac{x + \sin x}{1 + \cos x} \text{ dx }\]
\[\int \sin^3 \sqrt{x}\ dx\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}} dx\]
\[\int e^x \left[ \sec x + \log \left( \sec x + \tan x \right) \right] dx\]
\[\int x^2 \sqrt{a^6 - x^6} \text{ dx}\]
\[\int\left( x + 1 \right) \sqrt{x^2 + x + 1} \text{ dx }\]
\[\int\frac{1}{x\left[ 6 \left( \log x \right)^2 + 7 \log x + 2 \right]} dx\]
\[\int\frac{x}{\left( x - 1 \right)^2 \left( x + 2 \right)} dx\]
\[\int\frac{1}{x^4 - 1} dx\]
\[\int\frac{1}{\sin x + \sin 2x} dx\]
\[\int\frac{\cos 2x - 1}{\cos 2x + 1} dx =\]
\[\int \cos^3 (3x)\ dx\]
\[\int\frac{e^x - 1}{e^x + 1} \text{ dx}\]
\[\int\frac{1}{\text{ sin} \left( x - a \right) \text{ sin } \left( x - b \right)} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right)^3} dx\]
\[\int x \sin^5 x^2 \cos x^2 dx\]
Find : \[\int\frac{e^x}{\left( 2 + e^x \right)\left( 4 + e^{2x} \right)}dx.\]
\[\int\frac{x + 3}{\left( x + 4 \right)^2} e^x dx =\]
