Tentukan integral tak tentu berikut ini! ∫(x−x1)2dx

Ingat bahwa: ∫axndx=n+1axn+1+C,untukn=1 Sehingga diperoleh: ∫(x−x1)2dx======∫(x2−2+x21)dx∫(x2−2+x−2)dx2+11x2+1−0+12x0+1+−2+11x−2+1+C31x3−12x1+−11x−1+C31x3−2x−x−1+C31x3−2x−x1+C Dengan demikian, hasil dari adalah .

Tentukan integral tak tentu berikut ini! ∫(x−x1)...

Pertanyaan

Tentukan integral tak tentu berikut ini!

$\style{font-size:14px}{\int\left(x-\frac1x\right)^2\operatorname dx}$

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Ingat bahwa:

$integral subscript blank a x to the power of n d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C space comma space untuk space n not equal to 1$

Sehingga diperoleh:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses x minus 1 over x close parentheses squared d x end cell equals cell integral open parentheses x squared minus 2 plus 1 over x squared close parentheses d x end cell row blank equals cell integral open parentheses x squared minus 2 plus x to the power of negative 2 end exponent close parentheses d x end cell row blank equals cell fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 2 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent plus fraction numerator 1 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent plus C end cell row blank equals cell 1 third x cubed minus 2 over 1 x to the power of 1 plus fraction numerator 1 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus C end cell row blank equals cell 1 third x cubed minus 2 x minus x to the power of negative 1 end exponent plus C end cell row blank equals cell 1 third x cubed minus 2 x minus 1 over x plus C end cell end table end style$

Dengan demikian, hasil dari adalah Error converting from MathML to accessible text. .