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Question
`int e^{3x}/(e^{3x} + 1)`dx = ______
Options
3log|e3x + 1| + c
3log|e3x - 1| + c
`1/3log|e^{3x} + 1| + c`
`1/3log|e^{3x} - 1| + c`
MCQ
Fill in the Blanks
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Solution
`int e^{3x}/(e^{3x} + 1)`dx = `underline(1/3log|e^{3x} + 1| + c)`
Explanation:
Let I = `int e^{3x}/(e^{3x} + 1)`dx
Put e3x + 1 = t ⇒ 3e3x dx = dt
∴ I = `int1/t . (dt)/3 = 1/3log|t| + c`
= `1/3log|e^{3x} + 1| + c`
shaalaa.com
Some Special Integrals
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