Question

Calculus - need work shown

Answer 1

Easy evaluation!

`5( ln( |4x - 15| ) + c`

Explanation:

Feel free to ask if you're left with any doubts.

Answer 2

`\large \text4x-15`

Explanation:

`\large \displaystyle\begin{aligned}\textsf{let }\:u & =4x-15\\\implies (du)/(dx) & =4\\\implies dx & =(1)/(4)\: du\\\end{aligned}`

`\large\displaystyle\begin{aligned}\int (20)/(4x-5)\:dx &=\int (20)/(u)\cdot (1)/(4)\:du\\\\&=\int (20)/(4u)\:du\\\\&=\int (5)/(u)\:du\\\\&=5 \ln |u| +C\\\\&=5 \ln |4x-15| + C\end{aligned}`