- #1

Panphobia

- 435

- 13

## Homework Statement

[itex]\int \frac{t^{3}}{\sqrt{3 + t^{2}}}[/itex]

## Homework Equations

∫udv = uv - ∫vdu

## The Attempt at a Solution

So I tried integration by parts, then I had to integrate the last term with the same method, and then I got a u substitution integral, in the end I got.

[itex]\int \frac{t^{3}}{\sqrt{3 + t^{2}}}[/itex] = [itex]\frac{t^{4}}{\sqrt{3+t^{2}}\cdot 4} - \frac{t^{3}}{\sqrt{3+t^{2}}\cdot 2} - \sqrt[3/2]{3+t^{2}} +9\cdot \sqrt{3+t^{2}}[/itex]

This seems a little long for the space given for the question, so could someone confirm the correctness of this integral? Also how would I go about being more efficient in solving my integrals?

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