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Using integration by parts let U=x therefore du=dx.Let dv=5e^x therefore v=5e^x.answer = x*5e^x - integral(5e^x) = (x-1)(5e^x)

Using chain and product rule.dy/dx=(20x^3)cos(2x) - (10x^4)sin(2x)

Without even knowing M, the candidate can calculate M^5. This will follow from the fact that P is the matrix consisting of the eigenvectors of M as columns, and D will have the eigenvalues (in matching co...

This question involves forces and kinematics. First begin by drawing the situation and identifying the forces acting on the marble. The weight of the marble acts vertically downwards and is equal to the m...

We know from the properties of basic indices that a^-x=1/a^x, so 1/((5-2x³)²=(5-2x³)^-2 where in this case, a=5-2x³and x=2. Then t...