Question

integration of the given problem

Answer 1

\[\int\limits_{}^{}4\sin ^{5}x+5\sin ^{4}xdx/(x ^{5}+x+1)^{2}\]

Answer 2

uhhh....

Answer 3

oh ok

Answer 4

what type of math is this, algebra? i need to know if this is within my grade lv, im only a freshman in highschool.

Answer 5

sorry it will be
\[\int\limits_{}^{}(4x ^{5}+5x ^{4}_dx/(x ^{5}+x+1)^{2}\]

Answer 6

is this trig?

Answer 7

no.

Answer 8

srry can't help u. srry

Answer 9

@mukushla Help please!!

Answer 10

@.Sam. Help!!

Answer 11

\[\int\frac{4x^5+5x^4}{(x^5+x+1)^2}? \]

Answer 12

(.)_(.)

Answer 13

@Outkast3r09 Yeah!!

Answer 14

I have one guess

Answer 15

Split the top numerator and then +1-1

Answer 16

@Outkast, I did that, but the second half that you get - how to you proceed with that?

Answer 17

\[5x^4+4x^5\]

\[=5x^4+4x^5-1+1-x+x+x^5-x^5\]
\[=(1+x+x^5)(-1)+(1+x)(1+5x^4)\]
\[=(1+x+x^5)(-1)-(-1-x)(1+5x^4)\]

Answer 18

\[\int \frac{5x^4+1-1}{(x^5+x+1)^2}+\int\frac{4x^5}{(x^5+x+1)}\]

Answer 19

the second one you might be able to do partial fractions some miraculously way

Answer 20

have you tried partial fractions?

Answer 21

@Zarkon Can you please show the complete solution. please

Answer 22

i'm not sure zarkon is completely finished @ProgramGuru

Answer 23

\[\frac{4x^5+5x^4}{(1+x+x^5)^2}=\frac{(1+x+x^5)(-1)-(-1-x)(1+5x^4)}{(1+x+x^5)^2}\]

Answer 24

\[\frac{d}{dx}\left[\frac{-1-x}{1+x+x^5}\right]=\frac{(1+x+x^5)(-1)-(-1-x)(1+5x^4)}{(1+x+x^5)^2}\]

Answer 25

thus

\[\int\frac{4x^5+5x^4}{(1+x+x^5)^2}dx=\frac{-1-x}{1+x+x^5}+c\]

Answer 26

@Zarkon I'd give you 10 medals if i could

Answer 27

;)

Answer 28

@Zarkon awesome. If you had been my maths teacher, then i would have got a nobel prize for mathematics.

Answer 29

that would be amazing since there is no nobel prize for mathematics ;)

Answer 30

Maybe a Fields Medal though :)