Question

lf $I_n=\int \frac{t^n}{1+t^2}dt$ then $I_6+I_4=$

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

Answer 1

Answer: (A)

$\frac{t^5}{5}$

$I_n=\int \frac{t^n}{1+t^2}dt$

$I_6=\int \frac{t{}^6}{1+t^2}dt{I}_4=\int \frac{t{}^4}{1+t^2}dt$

$I_4+I_4=\int \frac{t^6}{1+t^2}dt+\int \frac{t^4}{1+t^2}dt$

$=\int \frac{t^4(1+t^2)}{1+t^2}dt$

$=\int t^4.dt$

$=\frac{t^5}{5}+c$

$I_6+I_4=\frac{t^5}{5}+c$