(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data:

using the substitution [itex]u=3x+4[/itex], work out:

[itex]\int 2x \sqrt{3x+4}[/itex]

2. The attempt at a solution:

[itex]\int 2x \sqrt{3x+4}[/itex]

[itex]u=3x+4 \rightarrow \mathrm{d}x = \frac{\mathrm{d}u}{3}[/itex]

[itex]\int \left( \frac{u-4}{3} \right)\left(u^{\frac12}\right) \ \frac{\mathrm{d}u}{3}[/itex]

[itex]\frac19 \int u^{\frac32} - 4u^{\frac12} \ \mathrm{d}u[/itex]

[itex]=\frac19 \left[ \frac{2u^{\frac52}}{5} - \frac{8u^{\frac32}}{3}\right] + c[/itex]

[itex]=\frac{2u^{\frac52}}{45} - \frac{8u^{\frac32}}{27}}+c[/itex]

[itex]=\frac{2(3x+4)^{\frac52}}{45} - \frac{8(3x+4)^{\frac32}}{27} + c[/itex]

3. The problem that I am encountering:

I was close to the answer but it is incorrect. The correct answer is:

[itex]\frac{4(3x+4)^{\frac52}}{45} - \frac{16(3x+4)^{\frac32}}{27} + c[/itex]

Where have I gone wrong? Thanks in advance.

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# Homework Help: Integration By Substitution

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