∫e3log⁡xx4+1−1dx is equal - Infinity Learn by Sri Chaitanya

A
$\log (x^{4} + 1) + C$
B
$\frac{1}{4} \log (x^{4} + 1) + C$
C
$- \log (x^{4} + 1) + C$
D
none of these

Solution:

We have,

$\begin{array}{l} I = \int e^{3 \log x} {(x^{4} + 1)}^{- 1} d x = \int \frac{e^{\log x^{3}}}{x^{4} + 1} d x = \int \frac{x^{3}}{x^{4} + 1} d x \\ \Rightarrow I = \frac{1}{4} \int \frac{1}{x^{4} + 1} d (x^{4} + 1) = \frac{1}{4} \log (x^{4} + 1) + C \end{array}$

$\int e^{3 \log x} {(x^{4} + 1)}^{- 1} d x$ is equal

Solution:

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