Question

Find the indefinite integral|(12x+5)dx

Answer 1

`\int {12x+5} \, dx`

For this problem, let's first apply the intergral sum rule.

`\int {12x+5} \, dx = \int{12x} \, dx + \int{5}x \,dx`

Then, we'll use the reverse power rule on each of these integrals.

`\int{12x} \,dx = 6x^2+C`

`\int{5} \,dx = 5x+C`

So the indefinite integral of
`\int{12x+5} \,dx` is
`6x^2+5x+C`.

Remember that we need our constant of integration,
`C`, because of if we take the derivative of a constant, it'll be 0.

Hope this helps!

Answer 2

Hi there!

`\int\limits {12x+5} \, dx`

Recall the following rules:

`\int\limits {x^n} \, dx = (x^(n+1))/(n+1)`

Use this rule to evaluate. Remember to include the constant:

`\int\limits {12x+5} \, dx = (12x^(1+1))/(1+1) + 5x +C`

`\int\limits {12x+5} \, dx = 6x^2 + 5x + C`