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Magazine Problem 273
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int(11 x-7)^{-3} d x $$
Problem 274
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int(7 x-11)^{4} d x $$
Problem 275
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int \cos ^{3} \theta \sin \theta d \theta $$
Problem 276
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int \sin ^{7} \theta \cos \theta d \theta $$
Problem 277
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int \cos ^{2}(\pi t) \sin (\pi t) d t $$
Problem 278
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int \sin ^{2} x \cos ^{3} x d x \quad\left(\operatorname{Hint} \sin ^{2} x+\cos ^{2} x=1\right) $$
Problem 279
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int t \sin \left(t^{2}\right) \cos \left(t^{2}\right) d t $$
Problem 280
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int t^{2} \cos ^{2}\left(t^{3}\right) \sin \left(t^{3}\right) d t $$
Problem 281
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int \frac{x^{2}}{\left(x^{3}-3\right)^{2}} d x $$
Problem 282
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int \frac{x^{3}}{\sqrt{1-x^{2}}} d x $$
