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Daniel
Daniel asked in Science & MathematicsMathematics · 9 years ago

By a change of variables, determine the indefinite integral as follows: integral (x + 5)(x^2 + 10x)^1/5dx?

integral (x + 5)(x^2 + 10x)^1/5dx

3 Answers

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  • ?
    Lv 5
    9 years ago
    Favorite Answer

    let x^2+10x= t

    on differentiating

    (2x+10) dx=`dt

    2(x+5) dx =dt

    so (x+5) dx = dt/2

    now the integral becomes integral dt/2

    t/2 +c

    (x^2+10x)/2 +c

  • Randy P
    Lv 7
    9 years ago

    The derivative of x^2 + 10x is 2x + 10 = 2(x + 5). So choosing u = x^2 + 10x will work well.

  • cidyah
    Lv 7
    9 years ago

    ∫ (x + 5)(x^2 + 10x)^(1/5) dx

    Let u = x^2+10x

    du = (2x+10) dx

    du = 2(x+5) dx

    (x+5) dx = (1/2) du

    ∫ (x + 5)(x^2 + 10x)^(1/5) dx = (1/2) ∫ u^(1/5) du

    = (1/2) u^(1/5+1) /(1/5+1)

    = (1/2) (5/6) u^(6/5) + C

    = (5/12) u^(6/5) + C

    = (5/12) (x^2+10x)^(6/5) + C

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