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

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

1 Answer

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Answer 1 · 2017-01-20T23:10:50

$\int t^{3} \sqrt{t^{4} + 5} d t = \frac{1}{6} (t^{4} + 5) \sqrt{t^{4} + 5} + C$ $int t^3 sqrt(t^4+5) dt = 1/6(t^4+5)sqrt(t^4+5) + C$

Explanation:

Substitute:

$x = t^{4} + 5$ $x = t^4+5$
$d x = 4 t^{3} d t$ $dx = 4t^3 dt$

so that the integral becomes:

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

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

1 Answer

Explanation:

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How do you integrate by substitution ∫t3√t4+5dtint t^3sqrt(t^4+5)dt?

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