Question

Evaluate the integral ∫ dx x⁴.x⁹.

A) 1/14x¹⁴+C
B) 1/13x¹³+C
C) 1/15x¹⁵+C
D) 1/12x¹²+C

Answer 1

The integral ∫ dx / (x⁴ ⋅ x⁹) simplifies to ∫ x⁽¹⁳ dx, which is evaluated using the power rule of integration to yield 1/14x¹⁴+C.

Step-by-step explanation:

To evaluate the integral ∫ dx / (x⁴ ⋅ x⁹), we first simplify the integrand by combining the powers of x: x⁴ ⋅ x⁹ = x¹⁳. The integral then becomes:

∫ dx / x¹⁳ = ∫ x⁽¹⁳ dx

Now, we use the power rule of integration, which states that ∫ x⁽ dx = 1/(n+1) ⋅ x⁽⁺¹ + C, where n is not equal to -1 and C is the constant of integration.

Applying this rule here:

∫ x⁽¹⁳ dx = 1/14 ⋅ x¹⁴ + C

Therefore, the correct answer is A) 1/14x¹⁴+C.