Question

help me pls. it's our homework in integral calculus.

find the indefinite integral of the ff. using inverse trigonometric functions:
1. integral of {1/[(sqrtx)(sqrt(1-x))]} dx
2. integral of [2x/(x^2 + 6x + 3)] dx
3. integral of [x+5 /sqrt (9-(x-3)^2)] dx

Answer 1

for #1, complete the square in denominator

Answer 2

here are the "clear" eqns:
\[1. \int\limits_{}^{} \frac{ 1 }{ \sqrt{x} \sqrt{1-x} } dx\]
\[2. \int\limits_{}^{} \frac{ 2x }{ x^{2} + 6x + 3 } dx\]
\[3. \int\limits_{}^{} \frac{ x + 5 }{ \sqrt{9 - (x - 3)^{2}} } dx\]

Answer 3

@ganeshie8

Answer 4

complete the square