First slide

Methods of integration

Question

$\int \frac{x + 1}{x^{2} + 1} d x =$

Easy

A

$\frac{1}{2} \log | x^{2} - 1 | + \cos^{- 1} x + c$
B

$\frac{1}{2} \log | x^{2} - 2 | + \tan^{- 1} x + c$
C

$\frac{1}{2} \log | x^{2} + 1 | + \tan^{- 1} x + c$
D

$\frac{1}{2} \log | x^{2} - 1 | - \tan^{- 1} x + c$

Solution

$\int \frac{x}{x^{2} + 1} d x + \int \frac{1}{x^{2} + 1} d x$
= $\frac{1}{2} \log | x^{2} + 1 | + \tan^{- 1} x + c$

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