How do you integrate by substitution $int t^3sqrt(t^4+5)dt$ ?

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Answer 1 · 2017-01-20T23:10:50

$int t^3 sqrt(t^4+5) dt = 1/6(t^4+5)sqrt(t^4+5) + C$

Substitute:

$x = t^4+5$
$dx = 4t^3 dt$

so that the integral becomes:

$int t^3 sqrt(t^4+5) dt = 1/4 int sqrt(x)dx = 1/6xsqrt(x)+C = 1/6(t^4+5)sqrt(t^4+5) + C$

How do you integrate by substitution int t^3sqrt(t^4+5)dtint t^3sqrt(t^4+5)dt?