First slide

Introduction to integration

Question

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

Easy

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

$\begin{matrix} I = \int e^{3 \log x} {(x^{4} + 1)}^{- 1} dx = \int e^{\log x^{3}} {(x^{4} + 1)}^{- 1} dx \\ = \frac{1}{4} \int \frac{4 x^{3}}{(x^{4} + 1)} dx = \frac{1}{4} \log (x^{4} + 1) + c \end{matrix}$

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