Advertisements
Advertisements
प्रश्न
उत्तर
\[\int\frac{x}{\sqrt{x + 4}}dx\]
\[ = \int\left( \frac{x + 4 - 4}{\sqrt{x + 4}} \right)dx\]
\[ = \int\left( \sqrt{x + 4} - \frac{4}{\sqrt{x + 4}} \right)dx\]
\[ = \int \left( x + 4 \right)^\frac{1}{2} dx - 4\int \left( x + 4 \right)^{- \frac{1}{2}} dx\]
\[ = \frac{\left( x + 4 \right)^\frac{1}{2} + 1}{\frac{1}{2} + 1} - 4\frac{\left[ x + 4 \right]^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} + C\]
\[ = \frac{2}{3} \left( x + 4 \right)^\frac{3}{2} - 8 \left( x + 4 \right)^\frac{1}{2} + C\]
\[ = \left( x + 4 \right)^\frac{1}{2} \left[ \frac{2}{3}\left( x + 4 \right) - 8 \right] + C\]
\[ = \left( x + 4 \right)^\frac{1}{2} \left[ \frac{2x + 8 - 24}{3} \right] + C\]
\[ = \left( x + 4 \right)^\frac{1}{2} \left[ \frac{2x - 16}{3} \right] + C\]
\[ = \frac{2}{3}\left( x - 8 \right)\sqrt{x + 4} + C\]
APPEARS IN
संबंधित प्रश्न
Integrate the following w.r.t. x `(x^3-3x+1)/sqrt(1-x^2)`
\[\int\frac{\left\{ e^{\sin^{- 1} }x \right\}^2}{\sqrt{1 - x^2}} dx\]
\[\int\frac{\cot x}{\sqrt{\sin x}} dx\]
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integral :-
Evaluate the following integral :-
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate:\[\int\frac{x^2}{1 + x^3} \text{ dx }\] .
Evaluate:
Evaluate:\[\int\frac{\sec^2 \sqrt{x}}{\sqrt{x}} \text{ dx }\]
Evaluate:\[\int\frac{\cos \sqrt{x}}{\sqrt{x}} \text{ dx }\]
Evaluate:\[\int\frac{\log x}{x} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - x^2 + x - 1}{x - 1} \text{ dx }\]
Write the value of\[\int\sec x \left( \sec x + \tan x \right)\text{ dx }\]
Evaluate: \[\int\frac{1}{x^2 + 16}\text{ dx }\]
Evaluate: `int_ (x + sin x)/(1 + cos x ) dx`
Evaluate the following:
`int sqrt(5 - 2x + x^2) "d"x`
Evaluate the following:
`int sqrt(x)/(sqrt("a"^3 - x^3)) "d"x`
