Need help with these integrals

[Calculated Risk]

Q1: I=∫ f(x)= ∫ (2x^4+9x²+x-4)/(x³+4) dx

I tried dividing it into simpler fractions and got
f(x)=2x+(x²+x-4)/(x³+4x) , this is where I got stuck, don't know how to deal with the bulky fraction.

Q2: I=∫ln(t³+4)dt
I tried using partial integration, lable u as ln(t³+4) and dv as 1; which then lead me to a fraction I need to integrate that looks quite like the one from Q1: ∫(3t³)/(t³+4 )

I will post a file containing these questions. In my file, they are exercises 1.2 and 1.3-a.

 

[Deleted member 4993]

Q1: I=∫ f(x)= ∫ (2x^4+9x²+x-4)/(x³+4) dx

I tried dividing it into simpler fractions and got
f(x)=2x+(x²+x-4)/(x³+4x) , this is where I got stuck, don't know how to deal with the bulky fraction.

Q2: I=∫ln(t³+4)dt
I tried using partial integration, lable u as ln(t³+4) and dv as 1; which then lead me to a fraction I need to integrate that looks quite like the one from Q1: ∫(3t³)/(t³+4 )

I will post a file containing these questions. In my file, they are exercises 1.2 and 1.3-a.

We prefer you post ONE problem per thread. Please start a new thread with the second problem.

Q1: your OP [f(x)= ∫ (2x^4+9x²+x-4)/(x³+4)] does not match your work [2x + (x²+x-4)/(x³+4x)]

Please fix it and we will continue....

 

[Calculated Risk]

Sorry, I did not notice that. I will post one question per thread next time. I have already solved these two questions; thank you for reminding me.