2007-03-05 03:29:14 · 3 answers · asked by ♥ Lady in Pink ♥ 2 in Science & Mathematics ➔ Mathematics
could u also tell me how u got that? :D
2007-03-05 03:47:59 · update #1
1/(1 + sin(x))
Multiply and divide the expression by (1 - sin(x)).
The logic behind this is that fractions are always converted to non-fractions by multiplying and dividing them by some factor that eliminates the denominator. This comes with practice. In our case, the expression becomes:
(1 - sin(x)) / (1 - (sin(x))^2) = (1 - sin(x)) / (cos(x))^2 = (1 - sin(x)) * (sec(x)) ^ 2 = (sec(x)) ^2 - sec(x) * tan(x)
Integral [(sec(x)) ^2 - sec(x) * tan(x)] = Integral[(sec(x)) ^2] - Integral[sec(x) * tan(x)] = tan(x) - sec(x)
2007-03-05 13:58:13 · answer #1 · answered by Shashi 2 · 0⤊ 0⤋
Multiply and divide by 1-sin x and rewrite the denominator as cos^2 x. After you divide, you will find an integral you can do.
2007-03-05 14:08:22 · answer #2 · answered by mathematician 7 · 0⤊ 0⤋
tan x - sec x + c
2007-03-05 11:45:58 · answer #3 · answered by ag_iitkgp 7 · 0⤊ 0⤋