1 of 8 0-day streak

Anti-differentiate reciprocal and linear-reciprocal functions

Question 1 of 8

No calculator

Consider the following reciprocal integrand

f(u)=\frac{5}{\left(u\right)}

\int \frac{5}{\left(u\right)}\,du

The stated branch of the linear denominator is shown below

u < 0

(a)1 mark

Choose the anti-derivative family for the displayed integrand

The arbitrary additive constant is included in the family

F(u)=5\,\log_e\left(u\right) + C

F(u)=5\,\log_e\left|u\right|

F(u)=5\,\log_e\left|u\right| + C

F(u)=5\,\left(u\right)^{0} + C

(b)3 marks

Write the logarithmic term in the displayed form. Keep the linear expression inside the absolute value exactly equal to the original denominator, without rescaling it or reversing its sign. Enter K, A and B

K\log_e\left|A\,u+B\right|

Logarithmic coefficient K Coefficient A of u in the original denominator Constant B in the original denominator