Question

integral of x/(x^4 + 25)

Answer 1

\[u=x^2+25\implies du=?\]

Answer 2

2x dx, so dx = 1/2 du

Answer 3

1/2 integral of du/u

Answer 4

xdx=1/2du

Answer 5

yes

Answer 6

wait I typed it wrong sorry, it's x^4

Answer 7

\[\int\frac{xdx}{x^4+25}\]?

Answer 8

yes, do I somehow use the derivative of arctan?

Answer 9

yeah that should work

Answer 10

u=x^2

Answer 11

but derivative of arctan is 1/(x^2 + 1), so how do I get rid of the 25?

Answer 12

\[\int\frac{dx}{x^2+a^2}=\frac1a\tan^{-1}(\frac xa)+C\]if we want to prove that it will take a minute

Answer 13

1/5 arctan (x^2/5)?

Answer 14

careful, you have to make the u-sub first

Answer 15

very close

Answer 16

1/10 not 1/5 since 1/2 du = dx?

Answer 17

exactly, and don't forget +C if it's indefinite