How do you integrate #int cosxsqrtsinx# using substitution?
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To integrate ( \int \cos(x) \sqrt{\sin(x)} ) using substitution:

Let ( u = \sin(x) ), then ( du = \cos(x) dx ).

Rewrite the integral in terms of ( u ): [ \int \sqrt{u} , du ]

Integrate ( \sqrt{u} ) with respect to ( u ): [ \frac{2}{3} u^{3/2} + C ]

Substitute back for ( u ): [ \frac{2}{3} \sin^{3/2}(x) + C ]
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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