Ask and Answer for Siti M (integral)

Ask #01 10 April 2017
Assalamualaikum, kak mau tanya soal integral berikut

         $\\\int x^{3}(x^{2}+2)^{3}dx=$

Answer #01 10 April 2017
Waalaikumsalam, baik kakak jawab

       $\\\int 3x^{3}(x^{2}+2)^{3}dx \\ \\u=x^{2}+2 \\ \\du = 2xdx \\-----\textup{x}\frac{1}{2} \\ \\\frac{1}{2}du=xdx$

substitusikan

      $\\u=x^{2}+2 \\ \\x^{2}=u-2$

     $\\xdx=\frac{1}{2}du$
ke soal

    $\\=\int x^{2}x(x^{2}+2)^{3}dx \\ \\=\int (u-2)u^{3}\frac{1}{2}du \\ \\=\int (\frac{1}{2}u^{4}-u^{3})du \\ \\=\frac{1}{2}.\frac{1}{5}u^{5}-\frac{1}{4}u^4+c \\ \\=\frac{1}{10}u^{5}-\frac{1}{4}u^4+c$
    $\\=\frac{1}{40}u^{4}(4u-10)+c \\ \\=\frac{1}{40}(x^{2}+2)^{4}(4(x^{2}+2)-10)+c \\ \\=\frac{1}{40}(x^{2}+2)^{4}(4x^{2}-2)+c$

Semoga bermanfaat

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