[DTube] Integral of ∫ 3x^2+8 / x^3+4x dx with f'(x)/f(x)

In this video, we perform the integral of 3x²+8 / x³+4x with the f'(x)/f(x) rule...

We do this first by expressing the function as a quotient of 2 functions:

And realising that q'(x) = 3x^2 + 4, which is very similar to p(x) = 3x^2 + 8.

If we express p(x) as p(x) = 3x^2 + 4 + 4, then the quotient becomes...

p(x)/q(x) = 3x^2 + 4 / x^3+4x + 4 / x^3+4x = q'(x) / q(x) + 4 / x^3+4x

Calculus: Techniques of Integration

1. Integral of ∫4/(x³ + 4x)dx - do we need partial fractions?
2. Integral of ∫3x²+8/x³+4xdx with f'(x)/f(x)
3. The integral of sec(x) - Part 1
4. The integral of sec(x) - Part 2
5. Reduction Formula for the Integral of ∫tanⁿ(x)dx
6. Integral of tan³(x)
7. Reduction formula for Integral of ∫sinⁿ(x)dx
8. Integral of 1/√e^2x+1

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