Question

integration of x^2+2x

Answer 1

use the rule of x^n = x^(n+1)/n+1 and same for 2x the answer would be..
x^3/3+2x^2/2+c

Answer 2

∫ ( x² + 2x ) dx

Applying Linearity, we get,

=> ∫ x² dx + 2 ∫ x dx => Equation 1

Now solving for ∫ x² dx

Applying Power rule,

xⁿ = xⁿ ⁺ ¹ / n + 1

=> In our case, n = 2

=> x² = x² ⁺ ¹ / 2 + 1

=> x² = x³ / 3

=> ∫ x² dx = x³ / 3

Now solving for 2 ∫ x dx

Applying Formula rule with n = 1 , we get,

=> x¹ + 1 / 1 + 1

=> x² / 2

=> 2 ∫ x dx = 2 * x² / 2 => x²

Substituting in Equation 1 we get,

=> x³ / 3 + x²

=> ∫ ( x² + 2x ) = x³ / 3 + x² + C.

Hence solved !