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f(x)=(4x^2-8)^(3/2)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫ (4x2−8)32dx\int\:\left(4x^2-8\right)^{\frac{3}{2}}dx

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Final answer to the exercise

12ln⁡∣x+x2−2∣+2x2−2x+8(x3x2−2(2)32)−8⋅2(12+32)ln⁡∣x2+x2−22∣+82(12+32)ln⁡∣x2+x2−22∣+C112\ln\left|x+\sqrt{x^2-2}\right|+2\sqrt{x^2-2}x+8\left(\frac{x^3\sqrt{x^2-2}}{\sqrt{\left(2\right)^{3}}\sqrt{2}}\right)-8\cdot 2^{\left(\frac{1}{2}+\frac{3}{2}\right)}\ln\left|\frac{x}{\sqrt{2}}+\frac{\sqrt{x^2-2}}{\sqrt{2}}\right|+82^{\left(\frac{1}{2}+\frac{3}{2}\right)}\ln\left|\frac{x}{\sqrt{2}}+\frac{\sqrt{x^2-2}}{\sqrt{2}}\right|+C_1

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∫ (4x2−8)32 dx
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