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** Step-by-step Solution **

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We can solve the integral $\int\sqrt{\sin\left(x\right)}\cos\left(x\right)dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $\sin\left(x\right)$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

Learn how to solve discriminant of quadratic equation problems step by step online.

$u=\sin\left(x\right)$

Learn how to solve discriminant of quadratic equation problems step by step online. Solve the trigonometric integral int(sin(x)^1/2cos(x))dx. We can solve the integral \int\sqrt{\sin\left(x\right)}\cos\left(x\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \sin\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify.

** Final Answer

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