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anonymous

  • 5 years ago

Evaluate the indefinite integral: (x^4)sqrt(12 + x^5)dx

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  1. anonymous
    • 5 years ago
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    pleaaaaase i neeed the answer !!!!! thanks!!!

  2. anonymous
    • 5 years ago
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    integrate x^4 sqrt(12+x^5) dx For the integrand x^4 sqrt(x^5+12), substitute u = x^5+12 and du = 5 x^4 dx: = 1/5 integral sqrt(u) du The integral of sqrt(u) is (2 u^(3/2))/3: = (2 u^(3/2))/15+constant Substitute back for u = x^5+12: = 2/15 (x^5+12)^(3/2)+constant

  3. anonymous
    • 5 years ago
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    that's correct, did you understand it Nat? ^_^

  4. anonymous
    • 5 years ago
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    \[ \int\limits_{}^{}x^4\sqrt{x^5 + 12}dx\] take the following: \[u = x^5 + 12\] \[du = 5x^4dx\] now you'll have the following form : \[=1/5\int\limits_{}^{}\sqrt{u}du\] \[=1/5[2u^{3/2}/3] + c\] \[=[ 2(x^5+12)^{3/2}/15] + c\] just like what elouis has done :) I hope it's clearer now ^_^

  5. anonymous
    • 5 years ago
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    thank you so much! that helped a lot!

  6. anonymous
    • 5 years ago
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    nvm oops

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