Question

If $I_n=\int \frac{t^n}{1+t^2}dt,$ then $I_6+I_4=$
(where $C$ is integration constant)

• A. $\frac{t^7}{7}+C$
• B. $\frac{t^5}{5}+C$
• C. $\frac{t^6}{6}+C$
• D. $\frac{t^3}{3}+C$

Answer 1

The correct option is B $\frac{t^5}{5}+C$

Given : $I_n=\int \frac{t^n}{1+t^2}dt$
$I_6+I_4=\int \frac{t^6}{1+t^2}dt+\int \frac{t^4}{1+t^2}dt=\int \frac{t^6+t^4}{1+t^2}dt=\int \frac{t^4(t^2+1)}{1+t^2}dt=\int t^{4}dt$
$=\frac{t^5}{5}+C$