Question

Trig Sub

Answer 1

\[\int\limits_ . x^{4}/ 1+x^{10}\]

Answer 2

dx at the end

Answer 3

\[\Large \int \frac{x^4}{x^{10}+1}dx \]
I guess that is what it is isn't it?

Answer 4

\[\Large x^5=\tan\alpha \]
such that:
\[\Large \frac{dx}{d\alpha}=\frac{\sec^2\alpha}{5\sqrt[5]{\tan^4\alpha}} \]
try this substitution, it will work out quite well.

Answer 5

@Spacelimbus from yours, I got 5x^4dx = sec^2 d(alpha) and the numerator is sec^2 , why don't we just replace, and get int (1/5) d(alpha)? and have the result directly = 1/5 alpha, and replace alpha = arctan (x^5)

Answer 6

sorry, denominator = sec^2

Answer 7

What you mean @Hoa is the following right?:
Implicit differentiation of the RHS
\[\Large 5x^4\frac{dx}{d\alpha}= \sec^2\alpha \]
Such that:
\[\Large x^4 = \frac{1}{5}\sec^2\alpha\frac{d\alpha}{dx} \]
This substitution works too of course, for the numerator! It's even more elgant, thanks for pointing this out.

Answer 8

\[\Large \frac{1}{5}\int 1 \cdot d\alpha \]
Most likely everything cancels out (-:

Answer 9

yes, that 's what i mean

Answer 10

sure, good point

Answer 11

ahah.. am I right?

Answer 12

of course you are! (-:
\[\Huge \checkmark \]

Answer 13

bingo. i thought i forgot all of them. still work.