In Exercises 110, evaluate the definite integral.7 2 x dx x2 + 1

Step 1 of 3

In order to integrate, we could use method of substitution easily here. 

\(\int_{2}^{7} \frac{x d x}{x^{2}+1}\)      ……(1)

For the denominator, 

Substitute 

\(u=x^{2}+1\)     …..(2)

Differentiating both sides, 

\(\begin{aligned} d u & =2 x d x \\ d x & =\frac{d u}{2 x}  \end{aligned}\)

….. (3)

Substituting the value of \(d x\) and \(u\) in the equation (1)

\(\begin{array}{l} \int_{2}^{7} \frac{x d u}{2 x u} \\ \rightarrow \int_{2}^{7} \frac{d u}{2 u} \end{array}\)

….. (4)