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Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int(2-3 x)(3+2 x)(1-2 x) d x$

Solution:

$\Rightarrow \int(2-3 x)(3+2 x)(1-2 x) d x$

By multiplying,

$\Rightarrow \int\left(6-4 x-9 x-6 x^{2}\right) d x$

$\Rightarrow \int\left(6-13 x-6 x^{2}\right) d x$

By Splitting, we get,

$\Rightarrow \int 6 d x-\int 13 x d x-\int 6 x^{2} d x$

By using the formulas,

$\int \mathrm{x}^{\mathrm{n}} \mathrm{dx}=\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}$ and

$\int \mathrm{kdx}=\mathrm{kx}+\mathrm{c}$

We get,

$\Rightarrow 6 \mathrm{x}-\frac{13 \mathrm{x}^{1+1}}{1+1}-\frac{6 \mathrm{x}^{2+1}}{2+1}+\mathrm{c}$

$\Rightarrow 6 \mathrm{x}-\frac{13 \mathrm{x}^{2}}{2}-\frac{6 \mathrm{x}^{3}}{3}+\mathrm{c}$

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