Question

integration(x^2+2) dx​

Answer 1

Answer:

The answer is (x³/3 + 2x + C).

Step-by-step explanation:

Integrating the given expression;

∫ (x² + 2) dx;

Here, the terms in integrand are held together by sum sign.

So, using sum rule, we can write;

[∫ (x)² dx] + [∫ (2) dx];                                        (i)

The latter operand in the above expression can also be written as;

[∫ (2x⁰) dx];                      (since, x⁰ = 1)              (ii)

Thus, using equation (i) and (ii);

[∫ (x)² dx] +  [∫ (2x⁰) dx];                            

Using power rule, we can conclude;

= (x)²⁺¹/(2+1) + 2(x⁰)⁺¹/(0+1) + C;

= x³/3 + 2x + C;

That's all.