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Tentukanintegral tak tentu berikut: f. ∫ ( 3 x ​ − x x ​ + 2 ) d x

Tentukan integral tak tentu berikut:

f. 

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S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

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intergal tak tentu dari adalah .

 intergal tak tentu dari integral open parentheses 3 square root of x minus x square root of x plus 2 close parentheses d x adalah 2 x square root of x minus fraction numerator 2 x squared square root of x over denominator 5 end fraction plus 2 x plus straight C.

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Pembahasan

Rumus dasar integral yaitu: dengan sayarat , suatu konstanta Diperoleh penyelesaiannya yaitu: Dengan demikian,intergal tak tentu dari adalah .

Rumus dasar integral yaitu:

  • integral k x to the power of n space d x equals fraction numerator k over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus straight C dengan sayarat straight n not equal to negative 1
  • integral k space d x equals k x plus straight C, suatu konstanta

Diperoleh penyelesaiannya yaitu:

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

Dengan demikian, intergal tak tentu dari integral open parentheses 3 square root of x minus x square root of x plus 2 close parentheses d x adalah 2 x square root of x minus fraction numerator 2 x squared square root of x over denominator 5 end fraction plus 2 x plus straight C.

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