Advertisements
Advertisements
Question
`int{sqrtx(ax^2+bx+c)}dx`
Sum
Advertisements
Solution
`int{sqrtx(ax^2+bx+c)}dx`
Treat `sqrtx = x^(1/2) "and integrate term-by-term (power rule" intx^ndx = (x^(n+1))/(n+1)`
`intsqrtx(ax^2+bx+c)dx=a intx^(5/2)dx +b intx^(3/2)dx+c intx^(1/2)dx`
`= a . 2/7 x^(7/2)+ b . 2/5x^(5/2) + c . 2/3 x^(3/2) + C`
`=(2a)/7 x^(7/2) + (2b)/5 x^(5/2) + (2c)/3 x^(3/2) + C`
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
\[\int\frac{5 \cos^3 x + 6 \sin^3 x}{2 \sin^2 x \cos^2 x} dx\]
\[\int\frac{\tan x}{\sec x + \tan x} dx\]
\[\int \left( 2x - 3 \right)^5 + \sqrt{3x + 2} \text{dx} \]
\[\int\frac{1}{\sqrt{2x + 3} + \sqrt{2x - 3}} dx\]
\[\int \sin^2 \frac{x}{2} dx\]
\[\int\frac{\text{sin} \left( x - \alpha \right)}{\text{sin }\left( x + \alpha \right)} dx\]
\[\int\frac{1 - \cot x}{1 + \cot x} dx\]
\[\int\frac{1}{\sqrt{1 - x^2}\left( 2 + 3 \sin^{- 1} x \right)} dx\]
\[\int \sin^5\text{ x }\text{cos x dx}\]
\[\int\left( 4x + 2 \right)\sqrt{x^2 + x + 1} \text{dx}\]
\[\int \sin^4 x \cos^3 x \text{ dx }\]
\[\int \sin^5 x \text{ dx }\]
\[\int\frac{1}{\sin^3 x \cos^5 x} dx\]
` = ∫1/{sin^3 x cos^ 2x} dx`
\[\int\frac{x^2 - 1}{x^2 + 4} dx\]
\[\int\frac{e^x}{1 + e^{2x}} dx\]
\[\int\frac{\sin 2x}{\sqrt{\cos^4 x - \sin^2 x + 2}} dx\]
\[\int\frac{x - 1}{3 x^2 - 4x + 3} dx\]
\[\int\frac{2x + 5}{x^2 - x - 2} \text{ dx }\]
\[\int\frac{\left( 1 - x^2 \right)}{x \left( 1 - 2x \right)} \text
{dx\]
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
\[\int\frac{1}{\cos 2x + 3 \sin^2 x} dx\]
\[\int x e^{2x} \text{ dx }\]
\[\int x \text{ sin 2x dx }\]
\[\int\frac{\log x}{x^n}\text{ dx }\]
\[\int x\left( \frac{\sec 2x - 1}{\sec 2x + 1} \right) dx\]
\[\int\frac{\left( x \tan^{- 1} x \right)}{\left( 1 + x^2 \right)^{3/2}} \text{ dx }\]
\[\int\frac{3 + 4x - x^2}{\left( x + 2 \right) \left( x - 1 \right)} dx\]
\[\int\frac{x}{\left( x - 1 \right)^2 \left( x + 2 \right)} dx\]
\[\int\frac{1}{1 + x + x^2 + x^3} dx\]
\[\int\frac{1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\sqrt{\frac{x}{1 - x}} dx\] is equal to
\[\int\frac{x^9}{\left( 4 x^2 + 1 \right)^6}dx\] is equal to
\[\int x\sqrt{2x + 3} \text{ dx }\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int\frac{x^2}{x^2 + 7x + 10}\text{ dx }\]
\[\int\frac{\cos^7 x}{\sin x} dx\]
