Question

Evaluate \[ \int \frac{x^7-1} {x^8\sqrt{\,1-2x^7+7x^{14}\,}} \,dx. \]

• A. \[ \frac{\sqrt{1-2x^7+7x^{14}}}{7x^7}+c \]
• B. \[ \log\!\left(\sqrt{1-2x^7+7x^{14}}\right)+c \]
• C. \[ \frac1{x^8}-\frac1{x^{15}}+c \]
• D. \[ \sqrt{\frac1{x^8}-\frac2{x^7}+\frac7{x^{14}}}+c \]

Hint:

Whenever the integrand is of the form \[ \boxed{ \frac{f'(x)} {\sqrt{f(x)}}, } \] or resembles the derivative of a quotient involving \[ \sqrt{f(x)}, \] try differentiating the given options to identify the correct antiderivative.

Answer 1

The Correct Option is A