Mathematics

Solve :
$$\displaystyle \int x \sqrt{x-1 dx}$$


SOLUTION
$$\displaystyle \int x\sqrt {x-1}dx$$
By barts
$$=x\dfrac {2}{3}(x-1)^{3/2}-\displaystyle \int \dfrac {2}{3}(x-1)^{3/2} dx$$
$$=\dfrac {2x}{3}(x-1)^{3/2}-\dfrac {2}{3} \dfrac {(x-1)^{3/2 +1}}{\dfrac {3}{2}+1}+C$$
$$\dfrac {2x(4+1)^{3/2}}{3}-\dfrac {4}{15}(x-1)^{5/2}+C$$
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Subjective Medium Published on 17th 09, 2020
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