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MIT 18.01 Single Variable Calculus (OCW)

OpenStudy (anonymous):

how guys, can someone show me how to integrate xcos(x^2+1) if possible?

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OpenStudy (anonymous):

Use a substitution: Is there part of the integral that can be tweaked into being the derivative of another part? For instance, look at the inside portion of the cosine: \[x^2+1\]Notice how the derivative of that would be 2x? That's almost exactly what you see in the part of the equation before the cosine...so the suggestion is to rewrite the integral with the substitution of \[u=x^2+1, du=2x dx\] It should then become an elementary integration of cosine.

OpenStudy (anonymous):

Go here http://www.wolframalpha.com/input/?i=integrate+xcos%28x^2%2B1%29 and click "show steps"

OpenStudy (anonymous):

put t=x^2 +1;dt/dx=2x;Integral=\[\int\limits_{?}^{?}(1/2)\cos(t)dt=(1/2)sint=(1/2)\sin(x^2+1)\]

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