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Writing an integral down is only the first step. A toolkit of techniques can help find its value, from substitutions to trigonometry to partial fractions to differentiation.
Find the indefinite integral \(\displaystyle{ 43\int{x \ln x dx} },\) using \(C\) as the constant of integration.
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Evaluate the integral \(\displaystyle{ 128\int{x \cos 3x dx} },\) using \(C\) as the constant of integration.
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Find the indefinite integral \(\displaystyle{ \int{x \sqrt{x+19} dx} },\) using \(C\) as the constant of integration.
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Evaluate the integral \(\displaystyle{ 67\int{t^2 e^{3t} dt} },\) using \(C\) as the constant of integration.
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Evaluate the integral \(\displaystyle{ 43\int _{ 0 }^{ 1 }{ \arctan x dx } },\) using \(C\) as the constant of integration.
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