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chikafujiwara

[tex]\int {12x+5} \, dx[/tex]

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

[tex]\int {12x+5} \, dx = \int{12x} \, dx + \int{5}x \,dx[/tex]

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

[tex]\int{12x} \,dx = 6x^2+C[/tex]

[tex]\int{5} \,dx = 5x+C[/tex]

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

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

Hope this helps!

leena

Hi there!

[tex]\int\limits {12x+5} \, dx[/tex]

Recall the following rules:

[tex]\int\limits {x^n} \, dx = \frac{x^{n+1}}{n+1}[/tex]

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

[tex]\int\limits {12x+5} \, dx = \frac{12x^{1+1}}{1+1} + 5x +C[/tex]

[tex]\int\limits {12x+5} \, dx = 6x^2 + 5x + C[/tex]

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