Evaluate tan$6(8$x$)$ sec$4(8$x$)$ dx$.$ Solution If we separate one sec$2(8$x$)$ factor, we can express the remaining sec$2(8$x$)$ factor in terms of tangent using the identity sec$2(8$x$)=1$ tan$2(8$x$).$ We can then evaluate the integral by substituting u $=$ tan$(8$x$)$ so that du $=$ Incorrect: Your answer is incorrect. dx$.$ tan$6(8$x$)$ sec$4(8$x$)$ dx $=$ tan$6(8$x$)$ sec$2(8$x$)$ sec$2(8$x$)$ dx $=$ tan$6(8$x$)(1$ tan$2(8$x$))$ sec$2(8$x$)$ dx $=18$ u$6$ Correct: Your answer is correct. du $=18$ u$6$ Correct: Your answer is correct. du $=$ Incorrect: Your answer is incorrect. u$972$ C $=$ Correct: Your answer is correct. $172$ tan$9(8$x$)$ C