Mathematics

# Integrate the following functions w.r.t $X :(2x+1)\sqrt{x+2}$

##### SOLUTION
Let $I=\int (2x+1)\sqrt{x+2}dx$
Put $x+2=t$
$\therefore dx=dt$
Alos, $x=t-2$
$\therefore 2x+1=2(t-2)+1=2t-3$
$\therefore I=\displaystyle \int (2t-3)\sqrt{t}dt$
$=\displaystyle \int (2t^{\dfrac{3}{2}} - 3t^{\dfrac{1}{2}}) dt$
$=2\displaystyle \int t^{\dfrac{3}{2}}dt - 3 \int t^{\dfrac{1}{2}}dt$
$=2. \dfrac{t^\dfrac{5}{2}}{\left(\dfrac{5}{2}\right)} -3 \dfrac{t^{\dfrac{3}{2}}}{\left(\dfrac{3}{2}\right)}+c$
$=\dfrac{4}{5}(x+2)^{\dfrac{5}{2}}-2(x+2)^{\dfrac{3}{2}}+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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