Final answer to the problem
$\frac{2\sqrt{\left(3+x\right)^{3}}}{3}-\sqrt{3}x+C_0$
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Step-by-step Solution
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1
Expand the integral $\int\left(\sqrt{3+x}-\sqrt{3}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
$\int\sqrt{3+x}dx+\int-\sqrt{3}dx$
Learn how to solve integrals with radicals problems step by step online.
$\int\sqrt{3+x}dx+\int-\sqrt{3}dx$
Learn how to solve integrals with radicals problems step by step online. Integrate int((3+x)^(1/2)-3^(1/2))dx. Expand the integral \int\left(\sqrt{3+x}-\sqrt{3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sqrt{3+x}dx results in: \frac{2\sqrt{\left(3+x\right)^{3}}}{3}. The integral \int-\sqrt{3}dx results in: -\sqrt{3}x. Gather the results of all integrals.
Final answer to the problem
$\frac{2\sqrt{\left(3+x\right)^{3}}}{3}-\sqrt{3}x+C_0$
