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

User Simulacre
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\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!

User Mahmoud Ibrahim
by
8.8k points
0 votes

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

User Stuart
by
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