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anonymous
 5 years ago
evaluate the indefinite integral......x^9/ sqrt(3+x^5)..... i got pretty far but now i need help because im stuck at a certain point
anonymous
 5 years ago
evaluate the indefinite integral......x^9/ sqrt(3+x^5)..... i got pretty far but now i need help because im stuck at a certain point

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2x^9  this thing? sqrt(3+x^5)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im stuck at (1/5) integrate (u3) /sqrt(u)..................

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x^9 * sqrt(3+x^5)   sqrt(3+x^5) sqrt(3+x^5) =x^9

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x^9 ___________ sqrt3 +x^5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i got to the point where i have a split integration

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2x^9  u = 3+x^5; du = 5x^4 dx; du/5x^4 = dx sqrt(3+x^5) x^9 du x^5 du  =  5x^4 u^(1/2) 5 u^(1/2) what x=? u = 3+x^5; x^5 = u3 right u3 du  5 u^(1/2)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2\[\int\limits_{} \frac{1}{5} u(u^{1/2})  \int\limits_{} \frac{3}{5} u^{1/2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats where im at now .. then you have to split them and get the integral of u / 5 u ^(1/2)  3/ 5 u ^(1/2)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2u[u^(1/2)] = u^(1/2) right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2\[\frac{1}{5} \int\limits_{} u^{1/2}  \frac{3}{5} \int\limits_{} u^{1/2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for the first one that is ../.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0because to get rid of the half in the denominator you have to multiply by 2?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2\[\frac{u^{(\frac{1}{2} + 1)}}{5(\frac{1}{2} + 1)}  \frac{3u^{(\frac{1}{2}+1})}{5( \frac{1}{2}+1)}+C\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2there is no 1/2 in the denominator; thats an exponent :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ahhh pellet i see now ... so what now after thats ?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2\[\frac{2u \sqrt{u}}{15}  \frac{6}{5\sqrt{u}} + C\] if I kept track of everything..its easier on paper i spose :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2soooo close :) move that sqrt(u) back up top with the "6"

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2change all yor "u"s back into (x+x^5)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2the bottom of that side goes to 5(3/2) = 15/2...flip the 2 on top..... shortcut math really; the proper what is to multiply bythe reciprocal of the denominator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Possible intermediate steps: integral x^9/sqrt(3+x^5) dx For the integrand x^9/sqrt(x^5+3), substitute u = x^5 and du = 5 x^4 dx: = 1/5 integral u/sqrt(u+3) du For the integrand u/sqrt(u+3), substitute s = u+3 and ds = du: = 1/5 integral (s3)/sqrt(s) ds Expanding the integrand (s3)/sqrt(s) gives sqrt(s)3/sqrt(s): = 1/5 integral (sqrt(s)3/sqrt(s)) ds Integrate the sum term by term and factor out constants: = 1/5 integral sqrt(s) ds3/5 integral 1/sqrt(s) ds The integral of 1/sqrt(s) is 2 sqrt(s): = 1/5 integral sqrt(s) ds(6 sqrt(s))/5 The integral of sqrt(s) is (2 s^(3/2))/3: = (2 s^(3/2))/15(6 sqrt(s))/5+constant Substitute back for s = u+3: = 2/15 (u+3)^(3/2)(6 sqrt(u+3))/5+constant Substitute back for u = x^5: = 2/15 (x^5+3)^(3/2)(6 sqrt(x^5+3))/5+constant Which is equal to: = 2/15 (x^56) sqrt(x^5+3)+constant

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2and sqrt(u^3) = u sqrt(u)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wow thank you so much ...
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