Advertisements
Advertisements
प्रश्न
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
योग
उत्तर
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}}dx\]
\[ = \int \left( \frac{x^2 - 2x + x - 2}{\sqrt{x}} \right)dx\]
`=∫((x^2-x-2)/sqrt(x))dx`
\[ = \int\left( x^\frac{3}{2} - x^\frac{1}{2} - 2 x^{- \frac{1}{2}} \right)dx\]
\[ = \left[ \frac{x^\frac{3}{2} + 1}{\frac{3}{2} + 1} \right] - \left[ \frac{x^\frac{1}{2} + 1}{\frac{1}{2} + 1} \right] - 2\left[ \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} \right] + C\]
\[ = \frac{2}{5} x^\frac{5}{2} - \frac{2}{3} x^\frac{3}{2} - 4 x^\frac{1}{2} + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\sqrt{x}\left( 3 - 5x \right) dx\]
\[\int\frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} dx\]
\[\int \left( 2x - 3 \right)^5 + \sqrt{3x + 2} \text{dx} \]
\[\int\frac{1}{\left( 7x - 5 \right)^3} + \frac{1}{\sqrt{5x - 4}} dx\]
\[\int\frac{1}{\sqrt{x + 1} + \sqrt{x}} dx\]
\[\int\frac{1 + \cos 4x}{\cot x - \tan x} dx\]
\[\int \cos^2 \frac{x}{2} dx\]
` ∫ cos 3x cos 4x` dx
` ∫ {"cosec" x }/ { log tan x/2 ` dx
\[\int \sin^5\text{ x }\text{cos x dx}\]
\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[\ ∫ x \text{ e}^{x^2} dx\]
\[\int\frac{x + \sqrt{x + 1}}{x + 2} dx\]
` ∫ tan x sec^4 x dx `
\[\int\frac{1}{1 + x - x^2} \text{ dx }\]
\[\int\frac{e^x}{\sqrt{16 - e^{2x}}} dx\]
\[\int\frac{x^2 + x + 1}{x^2 - x + 1} \text{ dx }\]
\[\int\frac{x}{\sqrt{x^2 + x + 1}} \text{ dx }\]
\[\int\frac{1}{13 + 3 \cos x + 4 \sin x} dx\]
`int 1/(sin x - sqrt3 cos x) dx`
\[\int\frac{8 \cot x + 1}{3 \cot x + 2} \text{ dx }\]
\[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}} dx\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int e^x \cdot \frac{\sqrt{1 - x^2} \sin^{- 1} x + 1}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int\sqrt{2ax - x^2} \text{ dx}\]
\[\int\left( x - 2 \right) \sqrt{2 x^2 - 6x + 5} \text{ dx }\]
\[\int\frac{2x + 1}{\left( x + 1 \right) \left( x - 2 \right)} dx\]
\[\int\frac{x^2 + 6x - 8}{x^3 - 4x} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x + 1 \right)^2} dx\]
\[\int\frac{1}{x^4 + 3 x^2 + 1} \text{ dx }\]
The primitive of the function \[f\left( x \right) = \left( 1 - \frac{1}{x^2} \right) a^{x + \frac{1}{x}} , a > 0\text{ is}\]
\[\int\frac{x^3}{x + 1}dx\] is equal to
\[\int \tan^5 x\ dx\]
\[\int \sec^4 x\ dx\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int x\sqrt{1 + x - x^2}\text{ dx }\]
\[\int\frac{1}{\left( x^2 + 2 \right) \left( x^2 + 5 \right)} \text{ dx}\]
