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Magazine Problem 262
In the following exercises, find the antiderivative using the indicated substitution. $$ \int(x-1)^{5} d x ; u=x-1 $$
Problem 263
In the following exercises, find the antiderivative using the indicated substitution. $$ \int(2 x-3)^{-7} d x ; u=2 x-3 $$
Problem 264
In the following exercises, find the antiderivative using the indicated substitution. $$ \int(3 x-2)^{-11} d x ; u=3 x-2 $$
Problem 265
In the following exercises, find the antiderivative using the indicated substitution. $$ \int \frac{x}{\sqrt{x^{2}+1}} d x ; u=x^{2}+1 $$
Problem 266
In the following exercises, find the antiderivative using the indicated substitution. $$ \int \frac{x}{\sqrt{1-x^{2}}} d x ; u=1-x^{2} $$
Problem 267
In the following exercises, find the antiderivative using the indicated substitution. $$ \int(x-1)\left(x^{2}-2 x\right)^{3} d x ; u=x^{2}-2 x $$
Problem 269
In the following exercises, find the antiderivative using the indicated substitution. $$ \int \cos ^{3} \theta d \theta ; u=\sin \theta\left(\operatorname{Hint} \cos ^{2} \theta=1-\sin ^{2} \theta\right) $$
Problem 270
In the following exercises, find the antiderivative using the indicated substitution. $$ \int \sin ^{3} \theta d \theta ; u=\cos \theta\left(\operatorname{Hint} : \sin ^{2} \theta=1-\cos ^{2} \theta\right) $$
Problem 271
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int x(1-x)^{99} d x $$
Problem 272
In the following exercises, use a suitable change of variables to determine the indefinite integral. $$ \int t\left(1-t^{2}\right)^{10} d t $$
