Mathematics - Definite Integration Question with Solution | TestHub

$$\frac{d}{dx}F(x)=\frac{e^{\sin x}}{x}\text{ or }{\int }_1^4\frac{3}{x}{e}^{\sin x^3}dx={\int }_1^4\frac{3x^2}{x^3}{e}^{\sin x^3}dx$$ Let ${\mathrm{x}}^3=\mathrm{t},3{\mathrm{x}}^2\mathrm{dx}=\mathrm{dt}$ when $x=1,t=1\&x-4,t=64$ $$\begin{array}{rl}& \mathrm{F}(\mathrm{t})={\int }_1^{64}\frac{{\mathrm{e}}^{\sin t}}{\mathrm{t}}\mathrm{dt}={\int }_1^{64}\mathrm{F}(\mathrm{t})\mathrm{dt}=\mathrm{F}(64)-\mathrm{F}(1)\\ & \mathrm{K}=64\end{array}$$