Basic maths-calculus-Q10

+1 vote

\int \frac{x+1}{\sqrt{x+2}} dx  is 

(A)  (x+2)^{3/2} + 2(x+2)^{1/2}

(B)  \frac{2}{3}(x+2)^{3/2} + 2(x+2)^{1/2}

(C)  \frac{2}{3}(x+2)^{3/2} - 2(x+2)^{1/2}

(D)  \frac{2}{3}(x+2)^{3/2} - (x+2)^{1/2}

asked May 19 in Basic Maths by gbeditor (44,560 points)
reshown May 24 by gbeditor

1 Answer

0 votes
 
Best answer

Start by substituting denominator::

 

u=\sqrt{x+2}\\ \\ 1/2*(\sqrt{x+2})dx=du\\ \\ 1/(\sqrt{x+2})dx=2du\\ \\ \int 2(u^2-1)du\\ \\ 2(u^3/3-u)\\ \\ 2[(\sqrt{x+2})^3/3-\sqrt{x+2}\ ]\\ \\ 2/3(x+2)^{3/2}-2(x+2)^{1/2}\\ \\ \therefore Answer\ should\ be\ C

answered May 27 by deepak-gatebook (112,760 points)
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