Kay's Math: Integration by substituition

Following are some questions to practice integration
1.
$\int_{1}^{2} \frac{u du}{1+u^{2}}$

2.
$\int_{1}^{2} \frac{x^{2}dx}{\sqrt{2x+1}}$

3.
   $\int_{2}^{3} \frac{dx}{x\: ln x}$

4
   $\int_{1}^{2}\frac{x\;dx}{1+x^{2}}$

5
$\int_{1}^{2}\frac{ln(2x)\;dx}{x}$

6
   $\int_{0}^{1}\;z\:\sqrt{1-z^{2}}dz$

7
$\int \frac{e^\frac{1}{t}}{t^{2}}dt$
8
$\int_{\frac{\pi }{4}}^{\frac{\pi}{3}} sin^{2}\theta \;cos\:\theta\:d\theta$

9

$\int \frac{sin\:2x}{\sqrt{1+cos\:2x}}dx$

10
$\int \frac{sin\:2x}{1+sin\:x}dx$

Kay's Math

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Thursday, October 3, 2019

Integration by substituition

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