# How do you integrate # sqrt3sinx(cosx)^0.5#?

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To integrate √3sin(x)(cos(x))^0.5, you can use the substitution method. Let ( u = \cos(x) ). Then ( du = -\sin(x)dx ). So the integral becomes ( -\frac{\sqrt{3}}{2}\int u^{0.5}du ). Integrate ( u^{0.5} ) with respect to ( u ) and then substitute back for ( x ). This yields ( -\frac{2\sqrt{3}}{3}u^{1.5} + C ), where ( C ) is the constant of integration. Substituting back for ( u = \cos(x) ), the final answer is ( -\frac{2\sqrt{3}}{3}\cos^{1.5}(x) + C ).

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When evaluating a one-sided 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 one-sided 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 one-sided 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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