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f(x)=x^2(x^2-9)^(3/2)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫(x2(x2−9)32)dx\int\left(x^2\left(x^2-9\right)^{\frac{3}{2}}\right)dx

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Final answer to the exercise

13516ln⁡∣x+x2−9∣+1516xx2−9+572x2−9x3+1162x2−9x5−814ln⁡∣x+x2−93∣−94xx2−9−16x2−9x3+272ln⁡∣x+x2−93∣+32x2−9x+C1\frac{135}{16}\ln\left|x+\sqrt{x^2-9}\right|+\frac{15}{16}x\sqrt{x^2-9}+\frac{5}{72}\sqrt{x^2-9}x^3+\frac{1}{162}\sqrt{x^2-9}x^5-\frac{81}{4}\ln\left|\frac{x+\sqrt{x^2-9}}{3}\right|-\frac{9}{4}x\sqrt{x^2-9}-\frac{1}{6}\sqrt{x^2-9}x^3+\frac{27}{2}\ln\left|\frac{x+\sqrt{x^2-9}}{3}\right|+\frac{3}{2}\sqrt{x^2-9}x+C_1

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∫(x2(x2−9)32 )dx
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