Question

Please Can you Do QN 32.

Answer 1

Answer:

1/2 ( log3 - 1 )

Step-by-step explanation:

Solution-----> 1) Plz see the attachment

2) In second step we convert x² in to ( - x² )

3) Then we add and subtract 1 in numerator

4) In fourth step we change fraction in to partial fractions and then seperate in to two integrals

5) Then we use two formulee of intregation

∫ 1 dx = x + c

∫ dx / ( a² - x² ) = 1 / 2a log ( a + x ) / ( a - x ) + c

6) Then we put first upper limit and then put lower limit and get the answer .

Additional information----->

1) ∫ dx / ( a² + x² ) = ( 1 / a ) tan⁻¹ ( x /a ) + C

2)

∫ dx / ( x² - a² ) = ( 1 / 2a ) log | ( x - a ) / ( x + a ) | + C

3)

∫ dx / √( a² - x² ) = Sin⁻¹ ( x / a ) + C

4)

∫ dx / √( x² + a² ) = log { x + √( x² + a² ) } + C

5)

∫ dx / √( x² - a² ) = log { x + √( x² - a² ) } + c