Advertisements
Advertisements
प्रश्न
\[\int\left( 2 - 3x \right) \left( 3 + 2x \right) \left( 1 - 2x \right) dx\]
बेरीज
Advertisements
उत्तर
\[\int\left( 2 - 3x \right) \left( 3 + 2x \right)\left( 1 - 2x \right)dx\]
\[ = \int\left( 2 - 3x \right) \left( 3 - 6x + 2x - 4 x^2 \right)dx\]
\[ = \int\left( 2 - 3x \right) \left( - 4 x^2 - 4x + 3 \right)dx\]
\[ = \int\left( - 8 x^2 - 8x + 6 + 12 x^3 + 12 x^2 - 9x \right)dx\]
\[ = \int\left( 12 x^3 + 4 x^2 - 17x + 6 \right)dx\]
\[ = \frac{12 x^4}{4} + \frac{4 x^3}{3} - \frac{17 x^2}{2} + 6x + C\]
\[ = 3 x^4 + \frac{4}{3} x^3 - \frac{17}{2} x^2 + 6x + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{\cos x}{1 - \cos x} \text{dx }or \int\frac{\cot x}{\text{cosec } {x }- \cot x} dx\]
` ∫ {cosec x} / {"cosec x "- cot x} ` dx
If f' (x) = x + b, f(1) = 5, f(2) = 13, find f(x)
` ∫ {sec x "cosec " x}/{log ( tan x) }` dx
\[\int\frac{1 - \sin x}{x + \cos x} dx\]
\[\int x^3 \sin x^4 dx\]
\[\int\frac{e^{m \tan^{- 1} x}}{1 + x^2} dx\]
\[\int x^2 \sqrt{x + 2} \text{ dx }\]
` ∫ tan^3 x sec^2 x dx `
\[\int \cot^5 x \text{ dx }\]
\[\int \sin^5 x \text{ dx }\]
Evaluate the following integrals:
\[\int\frac{x^2}{\left( a^2 - x^2 \right)^{3/2}}dx\]
` ∫ {1}/{a^2 x^2- b^2}dx`
\[\int\frac{e^x}{\left( 1 + e^x \right)\left( 2 + e^x \right)} dx\]
\[\int\frac{\cos x - \sin x}{\sqrt{8 - \sin2x}}dx\]
\[\int\frac{2x + 5}{x^2 - x - 2} \text{ dx }\]
\[\int\frac{x^2 \left( x^4 + 4 \right)}{x^2 + 4} \text{ dx }\]
\[\int\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{\cos x}{\cos 3x} \text{ dx }\]
\[\int\frac{1}{4 + 3 \tan x} dx\]
\[\int\frac{8 \cot x + 1}{3 \cot x + 2} \text{ dx }\]
` ∫ sin x log (\text{ cos x ) } dx `
\[\int \sec^{- 1} \sqrt{x}\ dx\]
` ∫ x tan ^2 x dx
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int e^x \left( \frac{1 + \sin x}{1 + \cos x} \right) dx\]
\[\int e^x \left( \frac{\sin 4x - 4}{1 - \cos 4x} \right) dx\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx }\]
\[\int\left( 2x - 5 \right) \sqrt{x^2 - 4x + 3} \text{ dx }\]
\[\int\frac{1}{x\left( x - 2 \right) \left( x - 4 \right)} dx\]
\[\int\frac{x^2 + 1}{\left( x - 2 \right)^2 \left( x + 3 \right)} dx\]
\[\int\frac{1}{\sqrt{x} + \sqrt{x + 1}} \text{ dx }\]
\[\int\frac{x^3}{\left( 1 + x^2 \right)^2} \text{ dx }\]
\[\int\frac{1}{4 \sin^2 x + 4 \sin x \cos x + 5 \cos^2 x} \text{ dx }\]
\[\int\frac{1}{\sin x \left( 2 + 3 \cos x \right)} \text{ dx }\]
\[\int x \sec^2 2x\ dx\]
\[\int\frac{1}{x \sqrt{1 + x^n}} \text{ dx}\]
\[\int \tan^{- 1} \sqrt{x}\ dx\]
\[\int \left( \sin^{- 1} x \right)^3 dx\]
