Integration help

So is it safe to say that we can use integration by substitution???

I would simplify the integrand by factoring from the numerator, then dividing out the common factors of the numerator and denominator. Or you might find it easier to just split the fraction, then reduce each term.

carry out the division

Can' i just put √t on the numerator and make it t^-1/2 and multiply (t + 2t^2)t^-1/2 together and integrate????

Can' i just put √t on the numerator and make it t^-1/2 and multiply (t + 2t^2)t^-1/2 together and integrate????.....

Yes, that's another way of splitting the fraction.

yup.

you'd end up with

or

then im authorized to integrate after that step right?

Yes, now it is just a matter of applying the power rule term by term.

Quote:

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Originally Posted by asilvester635

So is it safe to say that we can use integration by substitution???

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You can do this with the help of integration by parts.

Now after simplification:



We divide this integration in two parts. First:



Then for we use integration by parts:





Now:



So:




Check:

integration (t + 2*t^2)/(t)^(1/2) dt - Wolfram|Alpha