Compute the integral of sin x/(1+cos x)^0.5.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll re-write the denominator of the fraction:

(1+cos x)^0.5 = sqrt(1+cos x)

You'll have to substitute the expression within brackets by another variable.

Let 1 + cos x = t

We'll differentiate both sides:

-sin x dx = dt => sin x dx = -dt

We'll evaluate the integral:

`int` sin xdx/sqrt(1+cos x) = `int` -dt/sqrt t

`int` -t^(-1/2)*dt = - t^(-1/2 + 1)/(-1/2 + 1) + C

`int` -t^(-1/2)*dt = - t^(1/2)/(1/2) + C

`int` -t^(-1/2)*dt = - 2 sqrt t + C

`int` sin xdx/sqrt(1+cos x) = -2 sqrt (1 + cos x) + C

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