UNIT $6$ EXAM $-$ Integration and Accumulation $(2021)$

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$12.{\displaystyle \underset{0}{\overset{2}{}}}\frac{x^2}{x+1}dx=$

$($A$)ln3$

$($B$)ln3+2$

$($C$)ln6$

$($D$)ln6+4$

$13.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^2-6x+18}=$

$($A$)arcsin(\frac{x-3}{3})+C$

$($B$)ln|x^2-6x+18|+C$

$($C$)\frac{1}{3}arctan(\frac{x-3}{3})+C$

$($D$)\frac{1}{3}arctan(x+3)+C$

$14.$ Evaluate the integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xse{c}^2(x^2)dx$

$($A$)tan(x^2)+C$

$($B$)sec(x^2)tan(x^2)+C$

$($C$)2tan(x^2)+C$

$($D$)\frac{1}{2}tan(x^2)+C$