Let J=4x^3+2x^3-6 x+3 x+5e^ x -2e^ x -9

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

J=4x^3+2x^3-6\cos x+3\cos x+5e^{x}-2e^{x}-9.

(i) Combine like terms in

J

and write it in its simplest form. (ii) Obtain the indefinite integral

\displaystyle\int J\,dx

. (iii) Verify your answer to part (ii) by differentiating the antiderivative and comparing it with the simplified integrand from part (i).