Mariana P.

asked • 12/01/21

Find the following integration

Integral of x^2√x+4 dx

Luke J.

Mariana P., does the square root encompass x + 4 or only x? It changes the final solution by a bit whether it is or isn't
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12/01/21

1 Expert Answer

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Daniel B. answered • 12/02/21

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Use the substitution

u = x+4

Then

x = u-4

dx = du


∫x²√(x+4)dx = ∫(u-4)²√u du

= ∫(u² - 8u + 16)√u du

= ∫u5/2du - 8∫u3/2du + 16∫u1/2du

= (2/7)u7/2 - 8(2/5)u5/2 + (32/3)u3/2

= (2/7)(x+4)7/2 - (16/5)(x+4)5/2 + (32/3)(x+4)3/2


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Luke J.

Fantastic solution! However, "Calculus cardinal sin" (this is entirely a joke haha), where is that "+ C"? Hahaha Indefinite integral so it really should be there
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12/02/21

Taylor B.

Thank you so much Luke!
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12/02/21

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