Mathematics

$$\displaystyle \int \frac{x^{5/2}}{\sqrt{1+x^{7}}}dx \displaystyle =\frac{1}{k}log\left ( x^{k}+\sqrt{1+x^{7}} \right )+C$$


ANSWER

3.5


SOLUTION
Substitute $$\displaystyle x^{7/2}=t$$
$$\displaystyle \therefore \frac{7}{2}x^{5/2}dx=dt$$
$$\displaystyle \therefore I=\int \frac{2}{7}\frac{dt}{\sqrt{1+t^{2}}}=\frac{2}{7}log\left ( t+\sqrt{1+t^{2}} \right )+C$$
$$\displaystyle =\frac{2}{7}log\left ( x^{7/2}+\sqrt{1+x^{7}} \right )+C$$
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