# How do you integrate #int e^(x^2)sin^2x^3 # using integration by parts?

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To integrate ( \int e^{x^2}\sin^2(x^3) ) using integration by parts, let: [ u = \sin(x^3) ] [ dv = e^{x^2} , dx ]

Then, differentiate ( u ) and integrate ( dv ) to find ( du ) and ( v ), respectively.

Afterward, use the integration by parts formula: [ \int u , dv = uv - \int v , du ]

Substitute the values of ( u ), ( v ), ( du ), and ( dv ) into the formula and perform the calculations to find the integral.

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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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