Final answer to the problem
$\frac{1}{2}x^2+2x^{3}+12x+C_0$
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1
Apply the formula: $x\left(a+b\right)$$=xa+xb$, where $a=3x^2$, $b=6$, $x=2$ and $a+b=3x^2+6$
$\int\left(x+6x^2+12\right)dx$
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$\int\left(x+6x^2+12\right)dx$
Learn how to solve problems step by step online. Integrate int(x+2(3x^2+6))dx. Apply the formula: x\left(a+b\right)=xa+xb, where a=3x^2, b=6, x=2 and a+b=3x^2+6. Expand the integral \int\left(x+6x^2+12\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2. The integral \int6x^2dx results in: 2x^{3}.
Final answer to the problem
$\frac{1}{2}x^2+2x^{3}+12x+C_0$
