Evaluate:

Question:

Evaluate: $\int(x+2) \sqrt{3 x+5} d x$

Solution:

Here multiply and divide the question by 3

We get

$\Rightarrow \frac{1}{3} \int 3(\mathrm{x}+2) \sqrt{3 \mathrm{x}+5} \mathrm{dx}$

$\Rightarrow \frac{1}{3} \int(3 \mathrm{x}+6) \sqrt{3 \mathrm{x}+5} \mathrm{dx}$

Add and subtract 1 from above equation

$\Rightarrow \frac{1}{3} \int(3 x+6+1-1) \sqrt{3 x+5} d x$

$\Rightarrow \frac{1}{3} \int(3 x+5-1) \sqrt{3 x+5} d x$

$\Rightarrow \frac{1}{3} \int(3 x+5)^{\frac{3}{2}} d x-\int \frac{1}{3} \sqrt{3 x+5} d x$

$\Rightarrow \frac{1}{3} \times \frac{2(3 x+5)^{\frac{5}{2}}}{3 \times 5}-\frac{2(3 x+5)^{\frac{3}{2}}}{3 \times 3}+C$

$\Rightarrow \frac{2(3 x+5)^{\frac{5}{2}}}{45}-\frac{2(3 x+5)^{\frac{3}{2}}}{9}+C$

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