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Firstly, you need to see what is being asked to do. You need to find a vector equation of a line.Remember that the vector equation of a line is represented as r = a + λb.r is any point on the line, a is a...

This requires your knowledge of integration by parts. The trick here is that lnx can also be written as lnx*1 (as any term multiplied by 1 is itself). We set u=lnx and dv/dx equal to 1. Hence from this we...

d[sec(x)]/dx -->d[1/cos(x)] -->( [d[1].cos(x) - d[cos(x)].1] ) / [cos(x)]^2 -->[0.cos(x) - -sin(x).1]/ [cos(x)]^2 -->sin(x)/[cos(x)]^2 -->tan(x)sec(x) <-- Final Answer

First, you use the substitution u=1+e^x which implies that du=e^x dx. Then, you factorise e^3x = e^2x e^x and replace e^x dx with du. Then by re...

First, use the substitution u=e^x (which implies dx=du/u) to make the integral ∫6/(u*(u+2)))du. Next seperate the fraction using partial fractions and expand to form 3∫1/u du - 3∫1/(u+2) du. Next integrat...