Advertisements
Advertisements
प्रश्न
\[\int \left( 3x + 4 \right)^2 dx\]
योग
उत्तर
\[\int \left( 3x + 4 \right)^2 dx\]
\[ = \int \left( 9 x^2 + 2 \times 3x \times 4 + 16 \right)dx\]
`= 9 ∫ x^2dx + 24 ∫ x dx + 16 ∫ dx`
\[ = 9\left[ \frac{x^3}{3} \right] + 24\left[ \frac{x^2}{2} \right] + 16x + C\]
\[ = 3 x^3 + 12 x^2 + 16x + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\left( 2^x + \frac{5}{x} - \frac{1}{x^{1/3}} \right)dx\]
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
\[\int\left( x^e + e^x + e^e \right) dx\]
\[\int\frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} dx\]
` ∫ {cosec x} / {"cosec x "- cot x} ` dx
\[\int \cos^{- 1} \left( \sin x \right) dx\]
\[\int \left( a \tan x + b \cot x \right)^2 dx\]
If f' (x) = x + b, f(1) = 5, f(2) = 13, find f(x)
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
Integrate the following integrals:
\[\int\text { sin x cos 2x sin 3x dx}\]
\[\int\frac{\sin 2x}{a^2 + b^2 \sin^2 x} dx\]
\[\int \tan^{3/2} x \sec^2 \text{x dx}\]
\[\int\frac{\cos x - \sin x}{1 + \sin 2x} dx\]
\[\ ∫ x \text{ e}^{x^2} dx\]
\[\int\frac{\sec^2 \sqrt{x}}{\sqrt{x}} dx\]
` ∫ 1 /{x^{1/3} ( x^{1/3} -1)} ` dx
\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]
\[\int\frac{\sec^2 x}{\sqrt{4 + \tan^2 x}} dx\]
\[\int\frac{1}{x\sqrt{4 - 9 \left( \log x \right)^2}} dx\]
\[\int\frac{2x}{2 + x - x^2} \text{ dx }\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int\frac{3 + 2 \cos x + 4 \sin x}{2 \sin x + \cos x + 3} \text{ dx }\]
\[\int\frac{x + \sin x}{1 + \cos x} \text{ dx }\]
\[\int\left( e^\text{log x} + \sin x \right) \text{ cos x dx }\]
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int e^x \left( \frac{1 + \sin x}{1 + \cos x} \right) dx\]
\[\int e^x \left[ \sec x + \log \left( \sec x + \tan x \right) \right] dx\]
\[\int e^x \left( \log x + \frac{1}{x^2} \right) dx\]
\[\int x\sqrt{x^2 + x} \text{ dx }\]
\[\int\frac{\left( x^2 + 1 \right) \left( x^2 + 2 \right)}{\left( x^2 + 3 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{x + 1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
\[\int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int\frac{1}{a + b \tan x} \text{ dx }\]
\[\int\frac{\cos x}{\frac{1}{4} - \cos^2 x} \text{ dx }\]
\[\int\sqrt{1 + 2x - 3 x^2}\text{ dx } \]
\[\int\left( 2x + 3 \right) \sqrt{4 x^2 + 5x + 6} \text{ dx}\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx}\]
\[\int\frac{1}{\left( x^2 + 2 \right) \left( x^2 + 5 \right)} \text{ dx}\]
