x{x+2} - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 29 of 271

Marks: +1, -0

x\sqrt{x+2}

Solution:

Let

I=\int x\sqrt{x+2}

Put

x + 2 = t

\Rightarrow dx = dt

. Also

x = t - 2

\therefore I=\int (t-2)\sqrt{t}dt

=\int (t^{3/2}-2t^{1/2})dt

=\frac{2}{5}t^{5/2}-2\times\frac{2}{3}t^{3/2}+C

=\frac{2}{5}(x+2)^{5/2}-\frac{4}{3}(x+2)^{3/2}+C

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