QUESTIONS: Integration using substitutions.
(5) \displaystyle\int_{-1}^1 {e^{\arctan x} \over 1+x^2} dx
(12) \displaystyle\int\sin x \cos(\cos x) dx
(15) \displaystyle\int_0^{1/2} {x\over \sqrt{1-x^2}} dx
(18) \displaystyle\int {e^{2x}\over 1+e^{4x}} dx
(19) \displaystyle\int e^{x+e^x} dx
(26) \displaystyle\int {3x^2-2\over x^3-2x-8} dx
(27) \displaystyle\int \cot x \ln (\sin x) dx
(43) \displaystyle\int e^x \sqrt{1+e^x} dx
(34) \displaystyle\int_{\pi/4}^{\pi/2} {1+4\cot x\over 4-\cot x} dx
SOLUTIONS
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Wednesday, 1 February 2006
Integration using substitution. (5) \displaystyle\int_{-1}^1 {e^{\arctan x} \over 1+x^2} dx (12) \displaystyle\int\sin x \cos(\cos x) dx (15) \displaystyle\int_0^{1/2} {x\over \sqrt{1-x^2}} dx (18) \displaystyle\int {e^{2x}\over 1+e^{4x}} dx (19) \displaystyle\int e^{x+e^x} dx (26) \displaystyle\int {3x^2-2\over x^3-2x-8} dx (27) \displaystyle\int \cot x \ln (\sin x) dx (43) \displaystyle\int e^x \sqrt{1+e^x} dx (34) \displaystyle\int_{\pi/4}^{\pi/2} {1+4\cot x\over 4-\cot x} dx
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