Evaluate the integral by answering the following

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

Problem

Evaluate the integral F(x)=∫{2(3x−2+4e3x)−5[sin⁡(2x)+1x]} dx\displaystyle F(x)=\int \Bigl\{2\bigl(3x^{-2}+4e^{3x}\bigr)-5\bigl[\sin(2x)+\frac{1}{x}\bigr]\Bigr\}\,dx by answering the following. (a) Rewrite the integral as a sum of separate standard integrals. (b) Obtain an explicit expression for F(x)F(x), including a single constant of integration CC. (c) If F(π)=10F(\pi)=10, determine the value of CC.

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