Consider the function

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

h(x)=5\bigl(3x^{4}-2x^{3}\bigr)-7\bigl(3x^{4}-2x^{3}\bigr)+4e^{2x}-6e^{2x}

. (i) Simplify

h(x)

before integrating. (ii) Find

\displaystyle \int h(x)\,dx

. (iii) Differentiate your answer to part (ii) and verify that it equals the simplified integrand obtained in part (i).