Integration with substitution Exercises

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Here we’ll practice finding integration with substitution.

$\int \sin ^4(x)\cos (x) \d x = \answer {\frac {1}{5} \sin ^5(x)+C}$

$\int \frac {\cos (\frac {1}{x})}{x^2} \d x = \answer {-\sin (\frac {1}{x})+C}$

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

$\int \frac {\sin (\sqrt {x})}{\sqrt {x}} \d x = \answer {-2\cos (\sqrt {x})+C}$

$\int (x+2)\sqrt {3x+7} \d x = \answer {2 (7 + 3 x)^{3/2} (16 + 9 x)/135+C}$