Advertisements
Advertisements
प्रश्न
\[\int \left( 2x - 3 \right)^5 + \sqrt{3x + 2} \text{dx} \]
बेरीज
Advertisements
उत्तर
\[\int\left[ \left( 2x - 3 \right)^5 + \sqrt{3x + 2} \right]dx\]
\[ = \int \left( 2x - 3 \right)^5 dx + \int \left( 3x + 2 \right)^\frac{1}{2} dx\]
\[ = \frac{\left( 2x - 3 \right)^{5 + 1}}{2\left( 5 + 1 \right)} + \frac{\left( 3x + 2 \right)^\frac{1}{2} + 1}{3\left( \frac{1}{2} + 1 \right)} + C\]
\[ = \frac{\left( 2x - 3 \right)^6}{12} + \frac{2}{9} \left( 3x + 2 \right)^\frac{3}{2} + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( \frac{m}{x} + \frac{x}{m} + m^x + x^m + mx \right) dx\]
\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
\[\int\frac{\sin^3 x - \cos^3 x}{\sin^2 x \cos^2 x} dx\]
\[\int\frac{x^3}{x - 2} dx\]
\[\int\frac{3x + 5}{\sqrt{7x + 9}} dx\]
` ∫ tan 2x tan 3x tan 5x dx `
\[\int\frac{\cos^3 x}{\sqrt{\sin x}} dx\]
\[\int\sqrt {e^x- 1} \text{dx}\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
\[\int\frac{\sec^2 x}{1 - \tan^2 x} dx\]
\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]
\[\int\frac{2x - 3}{x^2 + 6x + 13} dx\]
\[\int\frac{\left( 3\sin x - 2 \right)\cos x}{13 - \cos^2 x - 7\sin x}dx\]
\[\int\frac{x + 7}{3 x^2 + 25x + 28}\text{ dx}\]
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
\[\int\frac{x + 1}{\sqrt{x^2 + 1}} dx\]
\[\int\frac{1}{5 + 4 \cos x} dx\]
`int 1/(cos x - sin x)dx`
\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]
\[\int\frac{4 \sin x + 5 \cos x}{5 \sin x + 4 \cos x} \text{ dx }\]
\[\int x e^{2x} \text{ dx }\]
\[\int e^\sqrt{x} \text{ dx }\]
\[\int \sin^{- 1} \left( \frac{2x}{1 + x^2} \right) \text{ dx }\]
\[\int \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) \text{ dx }\]
\[\int\frac{x^2 + 6x - 8}{x^3 - 4x} dx\]
\[\int\frac{1}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)} dx\]
\[\int\frac{1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x^2 + 1}} \text{ dx }\]
\[\int\frac{1}{\left( 1 + x^2 \right) \sqrt{1 - x^2}} \text{ dx }\]
\[\int \text{cosec}^2 x \text{ cos}^2 \text{ 2x dx} \]
\[\int \cos^3 (3x)\ dx\]
\[\int \cot^5 x\ dx\]
\[\int\frac{1}{a + b \tan x} \text{ dx }\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx}\]
