First slide

Introduction to integration

Question

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

Easy

A

$\log \sqrt{x^{4} + 1} + C$
B

$\frac{1}{2} \log \sqrt{x^{4} + 1} + C$
C

$- \log \sqrt{x^{4} + 1} + C$
D

$N o n e o f t h e s e$

Solution

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

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