**Question**

**Introduction**

False friends are words in two languages that look/sound alike, but
differ significantly in meaning. Do you
know that there are also false friends in mathematics? Can you distinguish and explain the
difference between the two integrals?

**Solution**

The integrand on the left has the

__variable__*x*as the base and the__constant__e as the index. So we integrate it using the Power Law.
By contrast, for the integrand on the right, the base e is a

__constant__whereas the index is the__variable__*x*. Integrating e to the power of*x*is the eeeeeeeeeeeeeeeasiest. You just get back the same thing, plus the arbitrary constant of course.**Remark**

Many students make the mistake of trying to apply the Power Law for the exponential.
As a learner of mathematics, one needs
to cultivate the

*habit*of being*observant*and*paying attention to detail*. This is part of developing one’s*identity*and*character*which is important in life.**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

*****GCE ‘A’ Levels (revision)

* revision for IB Mathematics HL &
SL (revision)

* Advanced Placement (AP) Calculus AB
& BC

* University / College Calculus

* other syllabuses that involve integral
calculus

* whoever is interested