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

Exercise

∫ x61+x2dx\int\:\frac{x^6}{\sqrt{1+x^2}}dx

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Final answer to the exercise

−1116ln⁡∣1+x2+x∣+5161+x2x+524(1+x2)3x+16(1+x2)5x−98ln⁡∣1+x2+x∣−981+x2x−34(1+x2)3x+32ln⁡∣1+x2+x∣+3x21+x2(1+x2)+C0-\frac{11}{16}\ln\left|\sqrt{1+x^2}+x\right|+\frac{5}{16}\sqrt{1+x^2}x+\frac{5}{24}\sqrt{\left(1+x^2\right)^{3}}x+\frac{1}{6}\sqrt{\left(1+x^2\right)^{5}}x-\frac{9}{8}\ln\left|\sqrt{1+x^2}+x\right|-\frac{9}{8}\sqrt{1+x^2}x-\frac{3}{4}\sqrt{\left(1+x^2\right)^{3}}x+\frac{3}{2}\ln\left|\sqrt{1+x^2}+x\right|+\frac{3x}{2\sqrt{1+x^2}}\left(1+x^2\right)+C_0

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∫ x6√1+x2 dx
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