Question

solve this integral showing steps

Answer 1

\[\Large\bf\sf \int\limits \frac{\sec^2\sqrt{x}}{\sqrt{x}}\;dx\quad=\quad \int\limits \sec^2\color{royalblue}{\sqrt{x}}\left(\frac{1}{\sqrt{x}}\;dx\right)\]

Let \(\Large\bf\sf u=\sqrt{x}\)
Replacing only \(\Large\bf\color{royalblue}{\text{ this one}}\).

Answer 2

Find du, the other sqrtx will be part of it.

Answer 3

Do you remember the derivative of \(\Large\bf\sf \sqrt x\) ?
It's a good one to have memorized, shows up a lot.

Doing the power rule is kind of a burden, but you can do that if you need.

Answer 4

1/2 root x

Answer 5

\[\Large\bf\sf du=\frac{1}{2\sqrt x}dx\]Ok good.
We're not able to substitute this in just yet.
That 2 is causing trouble. Hmmm what can we do?

Answer 6

distribute ?

Answer 7

? :O Does distribute meannnn multiply?

Answer 8

I'm not sure if that's what you meant to say or not lol
but yes, we want to multiply the 2 to the other side.

Answer 9

no I ment like factor it from the integral sign ??

Answer 10

\[\Large\bf\sf 2du=\frac{1}{\sqrt x}dx\]