Evaluate the following integrals step by step and hence obtain the antiderivative of…

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

Problem

Evaluate the following integrals step by step and hence obtain the antiderivative of the complete expression. (i) Find

\int 5e^{3x}\,dx.

(ii) Find

\int -4\sec^2 x\,dx.

(iii) Hence determine

\int \bigl(5e^{3x}-4\sec^2 x\bigr)\,dx.