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Magazine Problem 132
Use the technique of completing the square to express each trinomial as the square of a binomial. $$ 2 x^{2}-8 x+3 $$
Problem 133
Use the technique of completing the square to express each trinomial as the square of a binomial. $$ -x^{2}-2 x+4 $$
Problem 134
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \frac{d x}{\sqrt{4-x^{2}}} $$
Problem 135
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \frac{d x}{\sqrt{x^{2}-a^{2}}} $$
Problem 136
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \sqrt{4-x^{2}} d x $$
Problem 137
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \frac{d x}{\sqrt{1+9 x^{2}}} $$
Problem 138
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \frac{x^{2} d x}{\sqrt{1-x^{2}}} $$
Problem 139
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \frac{d x}{x^{2} \sqrt{1-x^{2}}} $$
Problem 140
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \frac{d x}{\left(1+x^{2}\right)^{2}} $$
Problem 141
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \sqrt{x^{2}+9} d x $$
