Question

i'm sorry Mr. Math. but how did ∫(32t)/(1+16t^2) become ln(1+16t^2)+C.....what happened to the 32

Answer 1

You can use this formula \(\int \frac{f'(x)}{f(x)}dx=\ln{f(x)}\).

Answer 2

In other words, you can notice in the integral you gave that the top is the derivative of the bottom, and that means that its integral is nothing but ln of the bottom.

Answer 3

Does that make any sense?

Answer 4

For example \(\int \frac{2x}{x^2}=\ln(x^2)\).

Answer 5

+c of course.

Answer 6

Yes! Thanks a million!

Answer 7

Glad to help.