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Evaluate the integral (write on whiteboard, too complicated to write here)

Make sure integral is in terms of sines and cosines onlyFactor out sine of numerator and make fraction in terms of cosineSubstitution y=cos(x)Fractions decompositionAnother 2 substitutionsSolve

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Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.

Consider the curve y=x/(x+4)^0.5. (i) Show that the derivative of the curve is given by dy/dx= (x+8)/2(x+4)^3/2 and (ii) hence find the coordinates of the intersection between the left vertical asymptote and the line tangent to the curve at the origin.

Evaluate the integral (write on whiteboard, too complicated to write here)

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Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.

Consider the curve y=x/(x+4)^0.5. (i) Show that the derivative of the curve is given by dy/dx= (x+8)/2(x+4)^3/2 and (ii) hence find the coordinates of the intersection between the left vertical asymptote and the line tangent to the curve at the origin.

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