Integrating problems by hand

Question

Integrate.

Do this problem by hand (do not use the Table of Integrals).

∫(-18𝑥+23) / (4𝑥-3)(𝑥+4)𝑑𝑥=  ?  + C

Which strategy did you choose?

u-Substitution

Partial Fractions

Trig substitution

integration by parts

algebraic manipulation / direct integration

 

Answer 1

Use Partial Fractions:

(-18x + 23) / [(4x - 3)(x + 4)] = A / (4x-3) + B / (x+4)

So, -18x + 23 = A(x+4) + B(4x-3) = (A+4B)x + (4A-3B)

A + 4B = -18

4A - 3B = 23

Solve for A and B and integrate.

Answer 2

https://youtu.be/V5pQIBwkoqU?si=rEHUBCbYDwYrg_Ha

The sound didn't work but I think you can follow it anyway.