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## Answers (2)

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)

tan x - sec x + c