Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

x^8(10+x^9)^3 Calculate the indefinite integral?

4 Answers

Relevance
  • Favorite Answer

    x^8 * (10 + x^9)^3 * dx

    u = 10 + x^9

    du = 9x^8 * dx

    (1/9) * 9 * x^8 * dx * (10 + x^9)^3 =>

    (1/9) * du * u^3 =>

    (1/9) * u^3 * du

    Integrate

    (1/9) * (1/4) * u^4 + C =>

    (1/36) * (10 + x^9)^4 + C

  • Philip
    Lv 6
    2 months ago

    J = Int'l of x^8(10+x^9)^3dx.;

    Put u = 10+x^9. Then du/dx = 9x^8, ie., (1/9)du=(x^8)dx & J=(1/9)Int'l(u^3du)

    = (1/36)u^4 + c, where c is an arbitrary constant of integration. Then indefinite

    integral is (1/36)(10+x^9)^4 + c.

  • Ian H
    Lv 7
    2 months ago

    Guess and correct like this

    Let y = (x^9 + 10)^4

    dy/dx = 36x^8(x^9 + 10)^3

    I = ∫x^8(10 + x^9)^3 dx = (1/36)(10 + x^9)^4 + C

  • 2 months ago

    Let u = 10 + x⁹

    Then, du = 9x⁸dx, and thus x⁸dx = (1/9)du

    ∫ x⁸ (10 + x⁹)³ dx

    = ∫ (10 + x⁹)³ (x⁸dx)

    = (1/9) ∫ u³ du

    = (1/9) (1/4) u⁴ + C

    = (1/36)(10 + x⁹)⁴ + C

Still have questions? Get your answers by asking now.