Advertisements
Advertisements
Question
\[\int\frac{1}{a^2 - b^2 x^2} dx\]
Sum
Advertisements
Solution
\[\int\frac{dx}{a^2 - b^2 x^2}\]
\[ = \frac{1}{b^2}\int\frac{dx}{\left( \frac{a^2}{b^2} \right) - x^2} \]
\[ = \frac{1}{b^2} \times \frac{1}{2\frac{a}{b}} \log \left| \frac{\frac{a}{b} + x}{\frac{a}{b} - x} \right| + C \left[ \therefore \int\frac{dx}{a^2 - x^2} = \frac{1}{2a} \log \left| \frac{a + x}{a - x} \right| + C \right]\]
` = \text{1}/{2ab} \text{ log }|{a + bx}/{a - bx}| + c `
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int \cos^{- 1} \left( \sin x \right) dx\]
If f' (x) = 8x3 − 2x, f(2) = 8, find f(x)
Write the primitive or anti-derivative of
\[f\left( x \right) = \sqrt{x} + \frac{1}{\sqrt{x}} .\]
\[\int \tan^2 \left( 2x - 3 \right) dx\]
\[\int\frac{1}{\text{cos}^2\text{ x }\left( 1 - \text{tan x} \right)^2} dx\]
\[\int\frac{x^2 + x + 5}{3x + 2} dx\]
\[\int\text{sin mx }\text{cos nx dx m }\neq n\]
\[\int\frac{\text{sin} \left( x - a \right)}{\text{sin}\left( x - b \right)} dx\]
\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]
\[\int 5^{x + \tan^{- 1} x} . \left( \frac{x^2 + 2}{x^2 + 1} \right) dx\]
\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[\int \tan^3 \text{2x sec 2x dx}\]
\[\int\frac{1}{\sin^4 x \cos^2 x} dx\]
` ∫ { x^2 dx}/{x^6 - a^6} dx `
\[\int\frac{x}{x^4 - x^2 + 1} dx\]
\[\int\frac{1}{x\sqrt{4 - 9 \left( \log x \right)^2}} dx\]
\[\int\frac{a x^3 + bx}{x^4 + c^2} dx\]
\[\int\frac{x + 2}{2 x^2 + 6x + 5}\text{ dx }\]
\[\int\frac{\left( 1 - x^2 \right)}{x \left( 1 - 2x \right)} \text
{dx\]
\[\int\frac{x}{\sqrt{8 + x - x^2}} dx\]
\[\int\frac{5x + 3}{\sqrt{x^2 + 4x + 10}} \text{ dx }\]
\[\int\frac{1}{4 \cos x - 1} \text{ dx }\]
\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]
\[\int x \cos x\ dx\]
\[\int2 x^3 e^{x^2} dx\]
\[\int\left( 4x + 1 \right) \sqrt{x^2 - x - 2} \text{ dx }\]
\[\int\frac{1}{x\left( x - 2 \right) \left( x - 4 \right)} dx\]
\[\int\frac{18}{\left( x + 2 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{1}{\left( x + 1 \right)^2 \left( x^2 + 1 \right)} dx\]
\[\int\frac{\cos x}{\left( 1 - \sin x \right)^3 \left( 2 + \sin x \right)} dx\]
\[\int\frac{\left( x^2 + 1 \right) \left( x^2 + 2 \right)}{\left( x^2 + 3 \right) \left( x^2 + 4 \right)} dx\]
\[\int e^x \left( 1 - \cot x + \cot^2 x \right) dx =\]
If \[\int\frac{1}{\left( x + 2 \right)\left( x^2 + 1 \right)}dx = a\log\left| 1 + x^2 \right| + b \tan^{- 1} x + \frac{1}{5}\log\left| x + 2 \right| + C,\] then
\[\int\frac{\sin x}{\cos 2x} \text{ dx }\]
\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int\frac{1}{1 + 2 \cos x} \text{ dx }\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int\frac{\sin^2 x}{\cos^6 x} \text{ dx }\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx}\]
