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Question

Which of the following is/are true?
(where C is constant of integration)

A
a3xdx=a3x3lna+C
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B
e2x dx=e2x2+C
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C
cosec(x+2)dx=ln|cosec(x+2)+cot(x+2)|+C
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D
sec(3x+4)dx=ln|sec(3x+4)+tan(3x+4)|+C
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Solution

The correct option is B e2x dx=e2x2+C
(a) a3xdx=a3xlna×13+C
abxdx=abxlna×1b+C;a>0,b0

(b) e2x dx=e2x2+C
(eaxdx=eaxa+C,a0)

(c) cosec(x+2)dx=ln|cosec(x+2)+cot(x+2)|+C
(cosec(ax+b)dx=ln|cosec(ax+b)+cot(ax+b)|a+C,a0)

(d) sec(3x+4)dx=ln|sec(3x+4)+tan(3x+4)|3+C
(sec(ax+b) dx=ln|sec(ax+b)+tan(ax+b)|a+C,a0)

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