Advertisements
Advertisements
प्रश्न
Find: `int (3x +5)/(x^2+3x-18)dx.`
बेरीज
उत्तर
Let `I = int ((3x+5))/(x^2 +3x -18)dx`
`I = int ((3x+5)dx)/((x+6) (x-3))`
let `(3x+5)/((x+6) (x-3)) = "A"/(x+6) + "B"/(x-3)`
so 3x + 5 = A (x -3) + B (x +6)
On comparing,
A + B = 3 ...(i)
-3A + 6B = 5 ...(ii)
-3A + 6(3 - A) = 5
-3A + 18 - 6A = 5
`"A" = -13/-9 = 13/9 and "B" = 3 - "A" = 3 - 13/9 = 14/9`
So, `int ((3x+5)dx)/((x+6)(x-3)) = int (13dx)/(9(x+6)) + int(14dx)/(9(x-3))`
= `13/9 "In" (x+6)+14/9"In"(x-3) + "C"`
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
\[\int\frac{x^5 + x^{- 2} + 2}{x^2} dx\]
Write the primitive or anti-derivative of
\[f\left( x \right) = \sqrt{x} + \frac{1}{\sqrt{x}} .\]
\[\int\sin x\sqrt{1 + \cos 2x} dx\]
\[\int \cos^2 \text{nx dx}\]
Integrate the following integrals:
\[\int\text { sin x cos 2x sin 3x dx}\]
\[\int\frac{\cos x}{\cos \left( x - a \right)} dx\]
\[\int\frac{1}{x (3 + \log x)} dx\]
\[\int\frac{\cos x}{2 + 3 \sin x} dx\]
\[\int\frac{\left( 1 + \sqrt{x} \right)^2}{\sqrt{x}} dx\]
\[\int\frac{e^{2x}}{1 + e^x} dx\]
\[\int\frac{1}{\left( x + 1 \right)\left( x^2 + 2x + 2 \right)} dx\]
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
` = ∫1/{sin^3 x cos^ 2x} dx`
\[\int\frac{1}{x^2 - 10x + 34} dx\]
` ∫ { x^2 dx}/{x^6 - a^6} dx `
\[\int\frac{\cos x - \sin x}{\sqrt{8 - \sin2x}}dx\]
\[\int\left( x + 1 \right) \text{ e}^x \text{ log } \left( x e^x \right) dx\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int\frac{e^x}{x}\left\{ \text{ x }\left( \log x \right)^2 + 2 \log x \right\} dx\]
\[\int\frac{1}{x \log x \left( 2 + \log x \right)} dx\]
\[\int\frac{x^2 + 1}{\left( x - 2 \right)^2 \left( x + 3 \right)} dx\]
\[\int\frac{1}{\sin x \left( 3 + 2 \cos x \right)} dx\]
\[\int\frac{1}{\sin x + \sin 2x} dx\]
\[\int\frac{\cos 2x - 1}{\cos 2x + 1} dx =\]
\[\int\frac{\sqrt{a} - \sqrt{x}}{1 - \sqrt{ax}}\text{ dx }\]
\[\int \log_{10} x\ dx\]
\[\int\frac{1 + x^2}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int\frac{5 x^4 + 12 x^3 + 7 x^2}{x^2 + x} dx\]
