Evaluate the integral.
-$$\int \frac { e ^ { \sin ^ { - 1 } 7 x } } { \sqrt { 1 - 49 x ^ { 2 } } } d x$$
A) $7 \mathrm { e } ^ { \sin ^ { - 1 } 7 \mathrm { x } } + \mathrm { C }$
B) $\frac { 1 } { 7 } \mathrm { e } ^ { \sin ^ { - 1 } 7 \mathrm { x } + \mathrm { C } }$
C) $\frac { 1 } { 7 } \mathrm { e } ^ { \cos ^ { - 1 } } 7 \mathrm { x } + \mathrm { C }$
D) $- \frac { 1 } { 7 } \mathrm { e } ^ { \cos ^ { - 1 } 7 \mathrm { x } } + \mathrm { C }$

Question

Quizplus · Accepted Answer

The integral is solved using the substitution $ u = \sin^{-1}(7x) $, which gives $ du = \frac{7}{\sqrt{1-49x^2}} dx $. This simplifies the integral to $\frac{1}{7} \int e^u \, du$, resulting in $\frac{1}{7} e^{\sin^{-1}(7x)} + C$.

Evaluate the Integral ∫esin⁡−17x1−49x2dx\int \frac { e ^ { \sin ^ { - 1 } 7 x } } { \sqrt { 1 - 49 x ^ { 2 } } } d x∫1−49x2​esin−17x​dx

Evaluate the Integral $\int \frac { e ^ { \sin ^ { - 1 } 7 x } } { \sqrt { 1 - 49 x ^ { 2 } } } d x$