Pertanyaan

∫ x x 2 ( 2 x − 3 )

$\int \frac{x ^{2} ( 2 x - 3 )}{x}$

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Klaim

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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Pembahasan

Integral tak tentu Jadi, .

Integral tak tentu

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator x squared open parentheses 2 x minus 3 close parentheses over denominator square root of x end fraction straight d x end cell equals cell integral fraction numerator x squared open parentheses 2 x minus 3 close parentheses over denominator x to the power of begin display style 1 half end style end exponent end fraction straight d x end cell row blank equals cell integral x squared x to the power of negative 1 half end exponent open parentheses 2 x minus 3 close parentheses straight d x end cell row blank equals cell integral x to the power of 2 minus 1 half end exponent open parentheses 2 x minus 3 close parentheses straight d x end cell row blank equals cell integral x to the power of 3 over 2 end exponent open parentheses 2 x minus 3 close parentheses straight d x end cell row blank equals cell integral 2 x to the power of 3 over 2 end exponent x minus 3 x to the power of 3 over 2 end exponent space straight d x end cell row blank equals cell integral 2 x to the power of 5 over 2 end exponent minus 3 x to the power of 3 over 2 end exponent space straight d x end cell row blank equals cell fraction numerator 2 over denominator 5 over 2 plus 1 end fraction x to the power of 5 over 2 plus 1 end exponent minus 3 over blank to the power of 3 over 2 plus 1 end exponent x to the power of 3 over 2 plus 1 end exponent plus C end cell row blank equals cell fraction numerator 2 over denominator 7 over 2 end fraction x to the power of 7 over 2 end exponent minus 3 over blank to the power of 5 over 2 end exponent x to the power of 5 over 2 end exponent plus C end cell row blank equals cell 2 times 2 over 7 times x cubed times square root of x minus 3 times 2 over 5 times x squared times square root of x plus C end cell row blank equals cell 4 over 7 x cubed square root of x minus 6 over 5 x squared square root of x plus C end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator x squared open parentheses 2 x minus 3 close parentheses over denominator square root of x end fraction straight d x end cell equals cell 4 over 7 x cubed square root of x minus 6 over 5 x squared square root of x plus C end cell end table$ .

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