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Solving: ∫0x1+t6dt\int_{0}^{x}\sqrt{1+t^6}dt
Solve instead: ∫0x(1+t6)dx\int_0^x\left(\sqrt{1+t^6}\right)dx

Exercise

∫0x(1+t6)dx\int_0^x\left(\sqrt{1+t^6}\right)dx

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Final answer to the exercise

(y−12)2+34(x1+x22+12ln⁡∣1+x2+x∣−(01+022+12ln⁡∣1+02+0∣))\sqrt{\left(y-\frac{1}{2}\right)^2+\frac{3}{4}}\left(\frac{x\sqrt{1+x^{2}}}{2}+\frac{1}{2}\ln\left|\sqrt{1+x^{2}}+x\right|- \left(\frac{0\sqrt{1+0^{2}}}{2}+\frac{1}{2}\ln\left|\sqrt{1+0^{2}}+0\right|\right)\right)

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∫0x(√1+t6)dx
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