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Albertoimus

  • 3 years ago

Evaluate the following indefinite integrals.

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  1. Albertoimus
    • 3 years ago
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  2. amoodarya
    • 3 years ago
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  3. RyanL.
    • 3 years ago
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    ^ oh yeah u substitution :D

  4. RyanL.
    • 3 years ago
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    @Albertoimus Do you get it? I know it looks a little messy but if you want I can rewrite so you can see it better.

  5. Albertoimus
    • 3 years ago
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    by all means.

  6. RyanL.
    • 3 years ago
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    \[\int\limits_{}^{}\frac{\cos \sqrt{x}}{\sqrt{x}}dx\] where we say that \[u=\sqrt{x}\]and if we square both sides that means that \[x=u^2\]and if we take the derivative of that we get \[dx=2u\]

  7. RyanL.
    • 3 years ago
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    The next step is a matter of replacing things

  8. RyanL.
    • 3 years ago
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    woops the last part should be \[dx=2udu\]

  9. RyanL.
    • 3 years ago
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    \[\int\limits_{}^{}\frac{cosu}{u}*2udu\] we cancel the u on the top with the u on the bottom. Also since 2 is a constant we take it outside the integral \[2\int\limits_{}^{}cosu*du\] the integral of cos u du is simply sin u \[2* \sin u\] And now we want it to convert it back into x instead of u and we know already that \[u=\sqrt{x}\] So it comes out as \[2*\sin \sqrt{x}\]

  10. RyanL.
    • 3 years ago
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    Done!

  11. Albertoimus
    • 3 years ago
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    thanks

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