How do you integrate #int e^x cos ^2 x^2 dx # using integration by parts?

Answer 1

You can't evaluate this integral by parts.

If you try #u = e^x#, then you'll need to integrate #cos^2(x^2) dx# which just uses a Frensel integral.
If you try #u = cos^2x^2#, then
#uv-int vdu = e^xcos^2x^2 + 4int x e^x sin(x^2) cos(x^2) dx#
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Answer 2

To integrate ( \int e^x \cos^2(x^2) , dx ) using integration by parts, we choose ( u = e^x ) and ( dv = \cos^2(x^2) , dx ). Then, we differentiate ( u ) to get ( du ) and integrate ( dv ) to get ( v ). After that, we apply 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 solve for the integral.

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Answer from HIX Tutor

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.

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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