Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 152
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 153
Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int_{-1}^{1}\left(1-x^{2}\right)^{3 / 2} d x $$
Problem 154
Use the substitutions \(x=\sinh \theta, \cosh \theta,\) or \(\tanh \theta\). Express the final answers in terms of the variable \(x\). $$ \int \frac{d x}{\sqrt{x^{2}-1}} $$
Problem 155
Use the substitutions \(x=\sinh \theta, \cosh \theta,\) or \(\tanh \theta\). Express the final answers in terms of the variable \(x\). $$ \int \frac{d x}{x \sqrt{1-x^{2}}} $$
Problem 156
Use the substitutions \(x=\sinh \theta, \cosh \theta,\) or \(\tanh \theta\). Express the final answers in terms of the variable \(x\). $$ \int \sqrt{x^{2}-1} d x $$
Problem 157
Use the substitutions \(x=\sinh \theta, \cosh \theta,\) or \(\tanh \theta\). Express the final answers in terms of the variable \(x\). $$ \int \frac{\sqrt{x^{2}-1}}{x^{2}} d x $$
Problem 158
Use the substitutions \(x=\sinh \theta, \cosh \theta,\) or \(\tanh \theta\). Express the final answers in terms of the variable \(x\). $$ \int \frac{d x}{1-x^{2}} $$
Problem 160
Use the technique of completing the square to evaluate the following integrals. $$ \int \frac{1}{x^{2}-6 x} d x $$
Problem 161
Use the technique of completing the square to evaluate the following integrals. $$ \int \frac{1}{x^{2}+2 x+1} d x $$
Problem 163
Use the technique of completing the square to evaluate the following integrals. $$ \int \frac{1}{\sqrt{-x^{2}+10 x}} d x $$
