Practicing Success
$∫\frac{dx}{(x+a)^{\frac{8}{7}}(x-b)^{\frac{6}{7}}}$ is equal to |
$(\frac{7}{a+b})(\frac{x+a}{x-b}^{\frac{1}{7}})+c$ $(\frac{7}{a+b})(\frac{x-b}{x+a}^{\frac{1}{7}})+c$ $\frac{6}{a+b}(\frac{x-b}{x+a}^{\frac{1}{6}})+c$ $\frac{6}{a+b}(\frac{x+a}{x-b}^{\frac{1}{6}})+c$ |
$(\frac{7}{a+b})(\frac{x-b}{x+a}^{\frac{1}{7}})+c$ |
Let $I=∫\frac{dx}{(x+a)^{\frac{8}{7}}(x-b)^{\frac{6}{7}}}=∫\frac{dx}{(x+a)^2(\frac{x-b}{x+a}^{\frac{6}{7}})}$. If $\frac{x-b}{x+a}=p$, then $\frac{a+b}{(x+a)^2}dx=dp⇒I=\frac{1}{a+b}∫\frac{dp}{p^{\frac{6}{7}}}$ $=\frac{7}{a+b}(p^{\frac{1}{7}})+c=(\frac{7}{a+b})(\frac{x-b}{x+a}^{\frac{1}{7}})+c$ Hence (B) is the correct answer. |