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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.2
Integrate the functions in Exercises 23 to 59.
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Question : 35 of 271
Marks: +1, -0
x2(2+3x3)3\frac{x^2}{(2+3x^3)^3}
Solution:  
I=∫x2(2+3x3)3dxI = \int \frac{x^2}{(2+3x^3)^3} dx
Put 2+3x3=t2 + 3x^3 = t ⇒9x2dx=dt\Rightarrow 9x^2 dx = dt
∴I=19∫dtt3=19∫t−3dt\therefore I = \frac{1}{9} \int \frac{dt}{t^3} = \frac{1}{9} \int t^{-3} dt =19t−2−2+C= \frac{1}{9} \frac{t^{-2}}{-2} + C
=−118t−2+C= -\frac{1}{18} t^{-2} + C =−118(2+3x3)2+C= -\frac{1}{18(2+3x^3)^2} + C
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