Question

find integral of the function x²-2x+1​

Answer 1

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Answer 2

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→find integral of the function x²-2x+1

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⇒$\displaystyle \int (x^2-2x+1) \: dx$

⇒$\displaystyle \int (x^2)dx \; - \int (-2x)dx \; + \int (1)dx$

⇒$\big[\frac{x^{2+1}}{2+1}\big] - 2\big[\frac{x^{1+1}}{1+1}\big] + 1\big[\frac{x^{0+1}}{0+1}\big]$

⇒$\frac{x^3}{3}-{\cancel{2}}\times \frac{x^2}{{\cancel{2}}} +1\times \frac{x}{1}$

⇒$\huge{\pink{\overbrace{\underbrace{\purple{\frac{x^{\small{3}}}{3}-x^{\tiny{2}}+x}}}}}$

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Formulas Used :-

$\displaystyle \int (x^n) \: dx$-

• $\Large{\fbox{\big[\frac{x^{n+1}}{n+1}\big]}}$

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