Evaluate the integrals $$\int (2-3x)(3+2x)(1-2x)dx$$

Asked by Sakshi | 1 year ago |  48

##### Solution :-

∫(2 – 3x)(3 + 2x)(1 – 2x) dx

= ∫(6 + 4x – 9x – 6x2)(1 – 2x) dx

= ∫(6 – 5x – 6x2)(1 – 2x) dx

= ∫(6 – 5x – 6x2 – 12x + 10x2 + 12x3) dx

= ∫(6 – 17x + 4x2 + 12x3) dx

Upon splitting the above, we have

= ∫6 dx – ∫17x dx + ∫4x2 dx + ∫12x3 dx

On integrating using formula,

∫xn dx =$$\dfrac{ x^{n+1}}{n+1}$$

we get

= 6x – $$\dfrac{17}{(1+1)}$$ x1+1 + $$\dfrac{4}{2+1}$$ x2+1 + $$\dfrac{12}{3+1}$$ x3+1 + c

= $$6x – \dfrac{17x^2}{2} +\dfrac{ 4x^3}{3} + 3x^4 + c$$

Answered by Aaryan | 1 year ago

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