Evaluate the indefinite integral. (Use C for the constant of integration.)
$\int \sin (t) \sqrt{1 + \cos (t)} d t$

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Therefore, the solution to the indefinite integral $\int \sin (t) \sqrt{1 + \cos (t)} d t$ is $- \frac{2}{3} (1 + \cos (t))^{\frac{3}{2}} + C$

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Step 1 ：Let's substitute $u = 1 + \cos (t)$

Step 2 ：Then, $d u = - \sin (t) d t$

Step 3 ：Now, let's rewrite the integral using the substitution: $\int \sin (t) \sqrt{1 + \cos (t)} d t = \int - \sqrt{u} d u$

Step 4 ：To solve this new integral, we can use the power rule for integration: $\int - \sqrt{u} d u = - \frac{2}{3} u^{\frac{3}{2}} + C$

Step 5 ：Substituting back $u = 1 + \cos (t)$ , we get: $- \frac{2}{3} (1 + \cos (t))^{\frac{3}{2}} + C$

Step 6 ：Therefore, the solution to the indefinite integral $\int \sin (t) \sqrt{1 + \cos (t)} d t$ is $- \frac{2}{3} (1 + \cos (t))^{\frac{3}{2}} + C$

Evaluate the indefinite integral. (Use C for the constant of integration.)∫sin⁡(t)1+cos⁡(t)dt

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Evaluate the indefinite integral. (Use C for the constant of integration.)
$\int \sin (t) \sqrt{1 + \cos (t)} d t$