Assessment: Methods of Integration

Find ∫5x⁴ dx.

Find ∫(eˣ − sin(x)) dx.

Find ∫3x²(x³+2)⁴ dx.

Find ∫x·ln(x) dx.

For 2/[(x−2)(x+3)] = A/(x−2) + B/(x+3), find the value of B.

Given 2/[(x−2)(x+3)] = (0.4)/(x−2) − (0.4)/(x+3), find ∫2/[(x−2)(x+3)] dx.

A factory's marginal cost is C'(x) = 6x + 2 dollars per unit, and fixed costs are C(0) = $50. Find the total cost C(10).

An engineer needs ∫t·e⁻ᵗ dt to find the total impulse of an exponentially-decaying force. Using u=t, dv=e⁻ᵗdt (so du=dt, v=−e⁻ᵗ), find the antiderivative.

Find ∫x²(x³−1)² dx.

Find ∫3/[(x−1)(x−4)] dx.