e³ x}(x^4+1)^{-1} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 244 of 271

Marks: +1, -0

e^{3\log x}(x^4+1)^{-1}

Solution:

Let

I=\int e^{3\log x}(x^4+1)^{-1}dx

=\int e^{\log x^3}(x^4+1)^{-1}dx

=\int x^3(x^4+1)^{-1}dx

=\int \frac{x^3}{x^4+1}dx

Put

x^4 = t

\Rightarrow 4x^3 dx = dt

\therefore I=\frac{1}{4}\int \frac{dt}{t+1}

=\frac{1}{4}\log(t+1)+C

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

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