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We can solve the integral $\int\frac{1\cos\left(x\right)}{\sqrt{1+\sin\left(x\right)}}dx$ by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of $t$ by setting the substitution
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$t=\tan\left(\frac{x}{2}\right)$
Learn how to solve definite integrals problems step by step online. Integrate the function (cos(x)1)/((1+sin(x))^1/2) from 0 to pi. We can solve the integral \int\frac{1\cos\left(x\right)}{\sqrt{1+\sin\left(x\right)}}dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.