Question

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

Answer 1

Hi there!

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

Recall the following rules:

$\int\limits {x^n} \, dx = \frac{x^{n+1}}{n+1}$

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

$\int\limits {12x+5} \, dx = \frac{12x^{1+1}}{1+1} + 5x +C$

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

Answer 2

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

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!