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Question
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
Options
True
False
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Solution
This statement is True.
Explanation:
Let 4ex – 25 = `A(2e^x - 5) + B d/(dx) (2e^x - 5)`
= 2exA – 5A + B(2ex)
2 × 2ex – 25 = 2ex (A + B) – 5A
∴ A + B = 2
And –25 = –5A
∴ A = 5
5 + B = 2
∴ B = 2 – 5 = – 3.
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