{1}{x²(x^4+1)³/4}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 232 of 271

Marks: +1, -0

\frac{1}{x^2(x^4+1)^{3/4}}

Solution:

Let

I = \int \frac{1}{x^2(x^4+1)^{3/4}}dx

= \int \frac{dx}{x^5\left(1+\frac{1}{x^4}\right)^{3/4}}

Put

1 + \frac{1}{x^4} = t

\Rightarrow -\frac{4}{x^5}dx = dt

\therefore I = -\frac{1}{4} \int \frac{dt}{t^{3/4}}

= -\frac{1}{4} \int t^{-3/4} dt

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

= -t^{1/4} + C

= -\left(1 + \frac{1}{x^4}\right)^{1/4} + C

Go to Question: