Indefinite Integrals Exercises

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so

Answer

This means

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We found that

So

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This means

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We found that

This means

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Take

Then apply the formula, keeping the limits of integration all the way through:

For the sake of tidiness and sanity, let's work out each of these pieces by itself.

Now we put things back together:

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Take

Then

Let's work out the first term:

And now the second term:

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Take

Apply the formula, keeping the limits of integration around:

Work out the first chunk:

And now work out the rest:

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We need to use the factor trick on this one. If we rewrite the integrand as

it's easier to see how to take the parts.

Take

u = x²

v' = 2xe^x2

u' = 2x

v = e^x2

Then we apply the formula:

Work out the first bit:

Now work out the new integral:

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Take

u = x

v' = e^x

u' = 1

v = e^x

Apply the formula:

If we want, we can play with the logs a little to make this prettier.