Question

Evaluate the following integration w.r.t. $x$
$\int [\frac{1}{(6x-5{)}^4}-\frac{1}{(8-3x{)}^9}]dx$

• A. $\frac{1}{18(6x-5{)}^3}-\frac{1}{24(8-3x{)}^8}+C$
• B. $\frac{-1}{18(6x-5{)}^3}-\frac{1}{24(8-3x{)}^8}+C$
• C. $\frac{1}{18(6x-5{)}^3}+\frac{1}{24(8-3x{)}^8}+C$
• D. $\frac{-1}{18(6x-5{)}^3}+\frac{1}{24(8-3x{)}^8}+C$

Answer 1

Answer: (B)

$\frac{-1}{18(6x-5{)}^3}-\frac{1}{24(8-3x{)}^8}+C$

According to question ,
$\int \frac{dx}{(6x-5{)}^4}-\int \frac{dx}{(8-3x{)}^9}$
Here is a linear equations in $x$,

Intergrating w.r.t to $x$:
=> $\frac{-1}{18(6x-5{)}^3}-\frac{1}{24(8-3x{)}^8}+C$