Question

Evaluate the integral: $\int e^{2\ln \left(x^2+1\right)}dx$

• A. $\frac{1}{5}{x}^5+\frac{3}{2}{x}^3+x+C$
• B. $5x^5+3x^3+x+C$
• C. $\frac{1}{5}{x}^5+\frac{2}{3}{x}^3+x+C$
• D. $2x+C$

Answer 1

Answer: (C)

$\int e^{2\ln \left(x^2+1\right)}dx=\int e^{\ln {\left(x^2+1\right)}^2}dx=\int {\left(x^2+1\right)}^{2}dx$
$=\int \left(x^4+2x^2+1\right)dx=\frac{1}{5}{x}^5+\frac{2}{3}{x}^3+x+C$