Find the general indefinite integral. (Use C for the constant of integration.)(x1.3 + 7x2.5) dx

To find the indefinite integral of the function (x^1.3 + 7x^2.5) dx, we use the power rule for integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

1. For the first term, x^1.3, we add 1 to the exponent to get 1.3 + 1 = 2.3. Then we divide 1 by the new exponent, 1/2.3 ≈ 0.43478. So, the integral of x^1.3 dx is approximately 0.43478x^2.3.

2. For the second term, 7x^2.5, we first take out the constant 7. Then we add 1 to the exponent to get 2.5 + 1 = 3.5. Then we divide 1 by the new exponent, 1/3.5 ≈ 0.28571. So, the integral of 7x^2.5 dx is approximately 7*0.28571x^3.5 = 2x^3.5.

3. Adding these two results together and adding the constant of integration C, we get the final answer: ∫(x^1.3 + 7x^2.5) dx ≈ 0.43478x^2.3 + 2x^3.5 + C.

To find the indefinite integral of the function (x^1.3 + 7x^2.5) dx, we use the power rule for integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

Step 1: Separate the integral into two parts: ∫x^1.3 dx + ∫7x^2.5 dx

Step 2: Apply the power rule to each part:

For ∫x^1.3 dx, n = 1.3, so the integral becomes (1/(1.3+1))x^(1.3+1) = (1/2.3)x^2.3

For ∫7x^2.5 dx, n = 2.5, so the integral becomes 7*(1/(2.5+1))x^(2.5+1) = (7/3.5)x^3.5 = 2x^3.5

Step 3: Add the constant of integration C to the result:

So, the indefinite integral of (x^1.3 + 7x^2.5) dx is (1/2.3)x^2.3 + 2x^3.5 + C.