{x³{{1-x^8}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

..... Miscellaneous Exercise .....
Integrate the functions in Exercises 229 to 252.

Question : 240 of 271

Marks: +1, -0

\frac{x^3}{\sqrt{1-x^8}}

Solution:

Let

I = \frac{x^3}{\sqrt{1-x^8}} dx

= \frac{1}{4} \int \frac{4x^3}{\sqrt{1-(x^4)^2}} dx

Let

x^4 = t

\Rightarrow 4x^3 dx = dt

\therefore I = \frac{1}{4} \int \frac{dt}{\sqrt{1-t^2}}

= \frac{1}{4} \sin^{-1} t + C

= \frac{1}{4} \sin^{-1}(x^4) + C

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