Question

Solve: ${\int }^{}\frac{12+3}{t+1}dt$

• A. $15\ln |t+1|+c$
• B. $-15\ln |t+1|+c$
• C. $15\ln |t-1|+c$
• D. $-15\ln |t-1|+c$

Answer 1

The correct option is A $15\ln |t+1|+c$

$I=\int \frac{15}{t+1}dt$

$I=15\int \frac{1}{t+1}dt$

Let $t+1=u$ $\Rightarrow dt=du$

$\Rightarrow I=15\int \frac{1}{u}du$

$\Rightarrow I=15\ln |u|+C$

$\Rightarrow I=15\ln |1+t|+C$