Advertisements
Advertisements
प्रश्न
\[\int\frac{1}{x^2 - 10x + 34} dx\]
योग
Advertisements
उत्तर
\[\int\frac{dx}{x^2 - 10x + 34}\]
\[ = \int\frac{dx}{x^2 - 10x + 25 - 25 + 34}\]
\[ = \int\frac{dx}{\left( x - 5 \right)^2 + 9}\]
\[ = \int\frac{dx}{\left( x - 5 \right)^2 + 3^2}\]
\[\text{ let x } - 5 = t\]
\[ \Rightarrow dx = dt\]
\[Now, \int\frac{dx}{\left( x - 5 \right)^2 + 3^2}\]
\[ = \int\frac{dt}{t^2 + 3^2}\]
\[ = \frac{1}{3} \tan^{- 1} \left( \frac{t}{3} \right) + C\]
\[ = \frac{1}{3} \tan^{- 1} \left( \frac{x - 5}{3} \right) + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int \left( 3x + 4 \right)^2 dx\]
\[\int\frac{1}{1 - \cos 2x} dx\]
\[\int\sin x\sqrt{1 + \cos 2x} dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
\[\int \sin^5\text{ x }\text{cos x dx}\]
\[\int\frac{\cos\sqrt{x}}{\sqrt{x}} dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
\[\int\left( 2 x^2 + 3 \right) \sqrt{x + 2} \text{ dx }\]
\[\int\frac{x^2 + 3x + 1}{\left( x + 1 \right)^2} dx\]
\[\ \int\ x \left( 1 - x \right)^{23} dx\]
\[\int \sin^4 x \cos^3 x \text{ dx }\]
\[\int\frac{1}{\sin x \cos^3 x} dx\]
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
` ∫ \sqrt{"cosec x"- 1} dx `
\[\int\frac{2x + 5}{x^2 - x - 2} \text{ dx }\]
\[\int\frac{x^2 + x + 1}{x^2 - x} dx\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{x - 1}{\sqrt{x^2 + 1}} \text{ dx }\]
\[\int\frac{3x + 1}{\sqrt{5 - 2x - x^2}} \text{ dx }\]
\[\int\frac{1}{\left( \sin x - 2 \cos x \right)\left( 2 \sin x + \cos x \right)} \text{ dx }\]
\[\int\frac{1}{\sin x + \sqrt{3} \cos x} \text{ dx }\]
\[\int\frac{1}{4 + 3 \tan x} dx\]
\[\int x \cos^2 x\ dx\]
\[\int \log_{10} x\ dx\]
\[\int e^x \cdot \frac{\sqrt{1 - x^2} \sin^{- 1} x + 1}{\sqrt{1 - x^2}} \text{ dx }\]
∴\[\int e^{2x} \left( - \sin x + 2 \cos x \right) dx\]
\[\int x^2 \sqrt{a^6 - x^6} \text{ dx}\]
\[\int\sqrt{3 - x^2} \text{ dx}\]
\[\int\frac{1}{x \log x \left( 2 + \log x \right)} dx\]
\[\int\frac{x^2 + 1}{\left( 2x + 1 \right) \left( x^2 - 1 \right)} dx\]
\[\int\frac{5 x^2 + 20x + 6}{x^3 + 2 x^2 + x} dx\]
\[\int\frac{1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int x^{\sin x} \left( \frac{\sin x}{x} + \cos x . \log x \right) dx\] is equal to
\[\int\frac{1}{\left( \sin^{- 1} x \right) \sqrt{1 - x^2}} \text{ dx} \]
\[\int \cot^5 x\ dx\]
\[\int\frac{1}{\sqrt{x^2 + a^2}} \text{ dx }\]
\[\int\frac{1}{x \sqrt{1 + x^n}} \text{ dx}\]
\[\int \left( \sin^{- 1} x \right)^3 dx\]
\[\int\frac{e^{m \tan^{- 1} x}}{\left( 1 + x^2 \right)^{3/2}} \text{ dx}\]
\[\int\frac{x + 3}{\left( x + 4 \right)^2} e^x dx =\]
