Expand the integral $\int\left(\frac{1}{2}x-1+\frac{\frac{5}{2}x+3}{2x^2+4x+3}\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
The integral $2\int\frac{\frac{5}{2}x+3}{2\left(\frac{1}{2}+\left(x+1\right)^2\right)}dx$ results in: $\frac{\sqrt{2}}{2}\arctan\left(1.414201\left(x+1\right)\right)+\frac{5}{4}\ln\left(\frac{1}{2}+\left(x+1\right)^2\right)$
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.