random

Question 1

a^x

Answer 1

a^x/lna

Question 2

∫1/(x2 - a2) dx

Answer 2

1/2a log|(x - a)(x + a| + C

Question 3

1/(a2 - x2) dx

Answer 3

1/2a log|(a + x)(a - x)| + C

Question 4

∫1/(x2 + a2) dx

Answer 4

= 1/a tan-1x/a + C

Question 5

∫1/√(x2 - a2)dx

Answer 5

= log |x +√(x2 - a2)| + C

Question 6

∫ √(x2 - a2) dx

Answer 6

= x/2 √(x2 - a2) -a2/2 log |x + √(x2 - a2)| + C

Question 7

∫1/√(a2 - x2) dx

Answer 7

= sin-1 x/a + C

Question 8

∫√(a2 - x2) dx

Answer 8

= x/2 √(a2 - x2) dx + a2/2 sin-1 x/a + C

Question 9

∫1/√(x2 + a2 ) dx

Answer 9

= log |x + √(x2 + a2)| + C

Question 10

∫ √(x2 + a2 ) dx

Answer 10

= x/2 √(x2 + a2 )+ a2/2 log |x + √(x2 + a2)|