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

Exercise

∫x+1x3dx\int\frac{\sqrt{x+1}}{x^3}dx

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Final answer to the exercise

12ln⁡∣x+1−1∣+32ln⁡∣x+1+1∣+−1x+1+1+38(x+1−1)+38ln⁡∣x+1−1∣+38(x+1+1)−38ln⁡∣x+1+1∣+−18(x+1−1)2+18(x+1+1)2+C0\frac{1}{2}\ln\left|\sqrt{x+1}-1\right|+\frac{3}{2}\ln\left|\sqrt{x+1}+1\right|+\frac{-1}{\sqrt{x+1}+1}+\frac{3}{8\left(\sqrt{x+1}-1\right)}+\frac{3}{8}\ln\left|\sqrt{x+1}-1\right|+\frac{3}{8\left(\sqrt{x+1}+1\right)}-\frac{3}{8}\ln\left|\sqrt{x+1}+1\right|+\frac{-1}{8\left(\sqrt{x+1}-1\right)^{2}}+\frac{1}{8\left(\sqrt{x+1}+1\right)^{2}}+C_0

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