calc

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find integral using table of integrals )
integral sin^4xdx
this the formula i used
integral sin^n xdx =-1/n sin^n-1xcosx +n-1/n integral sin^n-2

using the formula this is what i got: integral sin^4xdx=-1/4sin^3xcosx+3/4 integral sin^2xdx= -1/2sinxcosx+1/2 integral 1 dx
can someone please show me how to combine the two integrals to get the final answer.

  • calc -

    My answer, "|" = integral symbol

    |sin^4 x dx =
    -1/4 sin^3 x cos x + 3/4 (-1/2 sin x cos x + 1/2 | sin x dx )

    -1/4 sin^3 x cos x + 3/4 (-1/2 sin x cos x + 1/2 (-cos x)) + C

    -1/4 sin^3 x cos x + 3/4 (-1/2 sin x cos x - 1/2 cos x) + C

    -1/4 sin^3 x cos x - 3/8 sin x cos x
    - 3/8 cos x + C

  • calc -

    Hold on a few minutes, I might have a mistake.

  • calc -

    Mistake fixed below

    -1/4 sin^3 x cos x + 3/4 (-1/2 sin x cos x + 1/2 | 1 dx )

    -1/4 sin^3 x cos x + 3/4 (-1/2 sin x cos x + 1/2 x) + C

    -1/4 sin^3 x cos x - 3/8 sin x cos x
    + 3/8 x + C

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