evaluate given integral is:

$0$t$(6$si$+8$s$2$j$+7$k$)$ds$=$a$($t$)$i$+$b$($t$)$j$+$c$($t$)$k$\backslash$int$\_\{0\}^\{$t$\}\backslash$left$(6$s$\backslash$mathbf$\{$i$\}+8$s$^2\backslash$mathbf$\{$j$\}+7\backslash$mathbf$\{$k$\}\backslash$right$)$ ds $=$ a$($t$)\backslash$mathbf$\{$i$\}+$ b$($t$)\backslash$mathbf$\{$j$\}+$ c$($t$)\backslash$mathbf$\{$k$\}0$t$(6$si$+8$s$2$j$+7$k$)$ds$=$a$($t$)$i$+$b$($t$)$j$+$c$($t$)$k