Advertisements
Advertisements
प्रश्न
\[\int\frac{1}{x (3 + \log x)} dx\]
योग
Advertisements
उत्तर
` Here, we are" considering "log x as log_e x . `
\[\text{Let I} = \int\frac{1}{x\left( 3 + \log x \right)}dx\]
\[\text{Putting }\log x = t\]
\[ \Rightarrow \frac{1}{x} = \frac{dt}{dx}\]
\[ \Rightarrow \frac{dx}{x} = dt\]
\[ \therefore I = \int\frac{dt}{3 + t}\]
\[ = \text{log }\left| 3 + t \right| + C\]
\[ = \text{log }\left| 3 + \text{log x }\right| + C \left[ \because t = \text{log x} \right]\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\left( 3x\sqrt{x} + 4\sqrt{x} + 5 \right)dx\]
`int{sqrtx(ax^2+bx+c)}dx`
\[\int\sqrt{x}\left( x^3 - \frac{2}{x} \right) dx\]
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
\[\int \left( \tan x + \cot x \right)^2 dx\]
\[\int\frac{x^2 + 5x + 2}{x + 2} dx\]
\[\int \cos^2 \frac{x}{2} dx\]
` ∫ cos 3x cos 4x` dx
\[\int\frac{1}{ x \text{log x } \text{log }\left( \text{log x }\right)} dx\]
\[\int2x \sec^3 \left( x^2 + 3 \right) \tan \left( x^2 + 3 \right) dx\]
` ∫ tan^5 x dx `
\[\int \sin^3 x \cos^6 x \text{ dx }\]
\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]
\[\int\frac{dx}{e^x + e^{- x}}\]
\[\int x e^{2x} \text{ dx }\]
\[\int\cos\sqrt{x}\ dx\]
\[\int {cosec}^3 x\ dx\]
\[\int \cos^{- 1} \left( 4 x^3 - 3x \right) \text{ dx }\]
\[\int \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) \text{ dx }\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx }\]
\[\int\left( x + 1 \right) \sqrt{2 x^2 + 3} \text{ dx}\]
\[\int\left( 4x + 1 \right) \sqrt{x^2 - x - 2} \text{ dx }\]
\[\int\frac{3 + 4x - x^2}{\left( x + 2 \right) \left( x - 1 \right)} dx\]
\[\int\frac{1}{x \left( x^4 + 1 \right)} dx\]
\[\int\frac{1}{\sin x + \sin 2x} dx\]
Write the anti-derivative of \[\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right) .\]
\[\int x^{\sin x} \left( \frac{\sin x}{x} + \cos x . \log x \right) dx\] is equal to
\[\int\frac{x^3}{\sqrt{1 + x^2}}dx = a \left( 1 + x^2 \right)^\frac{3}{2} + b\sqrt{1 + x^2} + C\], then
\[\int \text{cosec}^2 x \text{ cos}^2 \text{ 2x dx} \]
\[\int\frac{e^x - 1}{e^x + 1} \text{ dx}\]
\[\int \sin^5 x\ dx\]
\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]
\[\int\sqrt{\text{ cosec x} - 1} \text{ dx }\]
\[\int\frac{1}{a + b \tan x} \text{ dx }\]
\[\int\frac{6x + 5}{\sqrt{6 + x - 2 x^2}} \text{ dx}\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int\frac{e^{m \tan^{- 1} x}}{\left( 1 + x^2 \right)^{3/2}} \text{ dx}\]
\[\int \sin^3 \left( 2x + 1 \right) \text{dx}\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
