We have, I=∫ _ #160; ^ #160; √( 1+ t^ 3 ) #160; dt I =∫ _ #160; ^ #160; ( 1+ t^ 3 ) #160; ^ 1/2 dt I =∫ _ #160; ^ #160; ( 1+ 1 ...

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Integration by Substitution

Evaluate ∫√...

Question

Evaluate
$\int \sqrt{1 + t^{3}} d t$

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Solution

We have,
$I = \int \sqrt{1 + t^{3}} d t I = \int {(1 + t^{3})}^{1 / 2} d t I = \int (1 + \frac{1}{2} t^{3} - \frac{1}{8} t^{6} . . . . . . .) d t I = (t + \frac{1}{8} t^{4} - \frac{1}{56} . t^{7} + . . . . . .) + C$

Hence, this is the answer.

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