Selesaikanlah :

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a). integral (x² + x) dx
b). integral (x3 + x) akar x^4+2x² dx
Ic). integral (sin tan – cos tan) dtan​

Selesaikanlah :

Selesaikanlah :

Jawab:

Penjelasan dengan langkah-langkah:

a) ∫(x^{2} +x) = ∫x^{2} dx + ∫ x dx

   = frac{1}{3} x^{3} + frac{1}{2} x^{2}

b) ∫(x^{3} + x) sqrt{x^{4}+2x^{2} } dx

   misalkan :

   u=sqrt{x^{4}+2x^{2} }

   = ∫frac{sqrt{u} }{4} du

   = frac{1}{4} ∫sqrt{u} du

   = frac{1}{4} ∫ x^{frac{1}{2} } du

   = frac{1}{4} frac{u^{frac{1}{2}+1 } }{frac{1}{2}+1 }

   = =frac{1}{4}cdot frac{left(x^4+2x^2right)^{frac{1}{2}+1}}{frac{1}{2}+1}

  = =frac{1}{6}x^3left(x^2+2right)^{frac{3}{2}}

 = =frac{1}{6}x^3left(x^2+2right)^{frac{3}{2}}+C

c) =int sin left(xright)dx-int cos left(xright)dx

  = =-cos left(xright)-sin left(xright)

  = =-cos left(xright)-sin left(xright)+C