MCQ
$\int {\,\,\frac{{1 - {x^7}}}{{x(1 + {x^7})}}} $ $dx $ equals :
- A$ln x + \frac{2}{7} ln (1 + x^7) + c$
- B$ln x - \frac{2}{7} ln (1 - x^7) + c$
- ✓$ln x - \frac{2}{7} ln (1 + x^7) + c$
- D$ln x + \frac{2}{7} ln (1 - x^7) + c$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f(t)=\left\{\begin{array}{cc}(-1)^{n+1} 2, & \text { if } t=2 n-1, n \in N , \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2 n-1 < t < 2 n+1, n \in N \end{array}\right.$
Define $g(x)=\int_1^x f(t) d t, x \in(1, \infty)$. Let $\alpha$ denote the number of solutions of the equation $g(x)=0$ in the interval $(1,8]$ and $\beta=\lim _{x \rightarrow 1+} \frac{g(x)}{x-1}$. Then the value of $\alpha+\beta$ is equal to. . . . . .