Question

1
----------dx list steps and notation used please!
1+4x^2

Answer 1

the integral of that

Answer 2

yes sorry, didn't know I can draw integrals here

Answer 3

$$
\large{
\int \frac{1}{1 + 4x^2}~dx
= \int \frac{1}{1 + (2x)^2}~dx



}


$$

Answer 4

you can do u-substitution
u = 2x

Answer 5

\[0.5\arctan2X+C\]

Answer 6

that's the answer

Answer 7

yes

Answer 8

should I do 1+U^2?

Answer 9

I didn't understand how to solve it....

Answer 10

what? how can you multiply the denominator by 2?

Answer 11

I understand, but why would you do so?

Answer 12

$$
\large{


u = 2x\\
du = 2dx\\
\frac{du}{2} = dx\\
~~~~~~~~~~~\\
\int \frac{1}{1 + (2x)^2}~dx =\int \frac{1}{1 + u^2}\cdot\frac{du}{2} = \frac{1}{2}\cdot \int \frac{1}{1 + u^2} \\
= \frac{1}{2} \arctan(u) + C = \frac{1}{2} \arctan(2x) + C


}

$$

Answer 13

Thanks allot! I think I've actually got it!