Question

To compute the integral ∫cos3(x)esin(x)dx, we should use first the substitution u= __________ to obtain the...

To compute the integral ∫cos3(x)esin(x)dx, we should use first the substitution u= __________ to obtain the integral ∫F(u)du, where F(u)= __________ To compute the integral ∫F(u)du, we use the method of integration by parts with

f(u)= __________ and g′(u)= __________ to get ∫F(u)du=G(u)−∫H(u)du , where G(u)= __________ and H(u)= __________ Now, to compute the integral ∫H(u)du, we need to use the method of integration by parts a second time with f(u)= __________ and g′(u)= __________ to get

∫H(u)du= __________ +C (Don't add the constant of integration C since we have done it for you.) We have then found that ∫F(u)du= __________ +C and hence ∫cos3(x)esin(x)dx= __________ +C

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