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f(x)=(4x^2)/((7+x^2)^(1/2)^(3/2))−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫4x27+x232dx\int\frac{4x^2}{\sqrt{7+x^2}^{\frac{3}{2}}}dx

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Final answer to the exercise

2(287(7)343)F(arctan⁡(x7)2∣2)+567x7+x243(7)3+−567F(arctan⁡(x7)2∣2)(7)34+C02\left(\frac{\frac{28\sqrt{7}}{\sqrt[4]{\left(7\right)^{3}}}}{3}\right)F\left(\frac{\arctan\left(\frac{x}{\sqrt{7}}\right)}{2}\Big\vert 2\right)+\frac{56\sqrt{7}x\sqrt[4]{7+x^2}}{3\sqrt{\left(7\right)^{3}}}+\frac{-56\sqrt{7}F\left(\frac{\arctan\left(\frac{x}{\sqrt{7}}\right)}{2}\Big\vert 2\right)}{\sqrt[4]{\left(7\right)^{3}}}+C_0

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∫4x2√7+x232  dx
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