Find the antiderivative of
Foundations:
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This problem requires three rules of integration. In particular, you need
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Integration by substitution (u - sub): If is a differentiable functions whose range is in the domain of , then
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We also need our power rule for integration:
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for .
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Solution:
Step 1:
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Use a u-substitution with This means , or . After substitution we have
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Step 2:
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We can no apply the power rule for integration:
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Step 3:
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Since our original function is a function of , we must substitute back into the result from step 2:
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Step 4:
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As will all indefinite integrals, don't forget the constant at the end.
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Final Answer:
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