#### Answer

$$6{\sin ^{ - 1}}\frac{x}{5} + C$$

#### Work Step by Step

$$\eqalign{
& \int {\frac{6}{{\sqrt {25 - {x^2}} }}dx} \cr
& {\text{take out the constant}} \cr
& = 6\int {\frac{1}{{\sqrt {25 - {x^2}} }}dx} \cr
& {\text{from the table 4}}{\text{.10 }}\int {\frac{{dx}}{{\sqrt {{a^2} - {x^2}} }}} = {\sin ^{ - 1}}\frac{x}{a} + C \cr
& {\text{letting }}a = 5 \cr
& = 6{\sin ^{ - 1}}\frac{x}{5} + C \cr
& {\text{check by differentiation}} \cr
& {\text{ = }}\frac{d}{{dx}}\left( {6{{\sin }^{ - 1}}\frac{x}{5} + C} \right) \cr
& {\text{ = 6}}\frac{d}{{dx}}\left( {{{\sin }^{ - 1}}\frac{x}{5}} \right) + \frac{d}{{dx}}\left( C \right) \cr
& {\text{ = }}6\left( {\frac{1}{{\sqrt {{{\left( 5 \right)}^2} - {x^2}} }}} \right) + 0 \cr
& = \frac{6}{{\sqrt {25 - {x^2}} }} \cr} $$