Question Bank - Mathematics

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Find the value of ? (2cos2x - 9x8 + 5e5x ) dx

A.
sin2x - x9 - e5x + C
B.
sin2x + x9 + e5x + C
C.
sin2x + x9 - e5x + C
D.
sin2x - x9 + e5x + C

Solution:

Concept:Some useful formulas are: ? cos(ax) dx = \(\rm sinax \over a\) + C? eax dx = \(\rm e^{ax} \over a\) + C\(\rm ? x^n dx = \frac {(x^{n+1})} {(n+1)} +C; \ n?1\)Calculation: ? (2cos2x - 9x8 + 5e5x ) dx= ? 2cos2x dx - ? 9x8 dx+ ? 5e5x dx= \(\rm 2\frac{sin2x}{2} - 9 \frac{x^9}{9} + 5\frac{e^{5x}}{5} + C\) ,where C is the constant of integration= sin2x - x9 + e5x + C

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