Mathematics OpenStudy (anonymous):

Integral of 1/(u^3 + 3u) du, without using partial fractions? Many thanks! OpenStudy (anonymous):

This can be done by some none obvious algebra manipulation: integral [ 1/(u^3 + 3u) du ] = 1/3 * integral [ 3/(u^3 + 3u) du ] =1/3 * integral [ 3/{u*(u^2+3) du ] =1/3 * integral [ {3+u^2-u^2} / {u*(u^2+3)} du ] =1/3*integral [ {3+u^2} / {u*(u^2+3)} du ] - 1/3*integral [ {u^2} / {u*(u^2+3)} du ] =1/3*integral [ 1/u du ] - 1/3*integral [ u/{u^2+3} du] let u^2+3 = t => dt = 1/(2*u) du =1/3*ln(u) - 1/3 * 1/2 * integral (1/t dt) =1/3*ln(u) - 1/3*1/2*ln(t) =1/3*ln(u) - 1/3*ln(sqrt(t)) =1/3*ln( u / sqrt(t) ) =1/3*ln( u / sqrt(u^2+3) ) + C

Latest Questions CancerGirl: hola everyone
4 minutes ago 0 Replies 0 Medals nabilah02: An object P travels from A to B in a time of 80 s. The diagram shows the graph of v against t, where vm su22121 is the velocity ofP at time ts after leaving
8 minutes ago 0 Replies 0 Medals SaltTheLoser: Does anyone want to do some edits?
1 hour ago 12 Replies 0 Medals mohd: evaluate the closed line integral of h about the rectangular path
49 minutes ago 5 Replies 0 Medals mohd: evaluate the closed line integral of h about the rectangular path
3 hours ago 0 Replies 0 Medals XxNoodlexX: How many chapters are too many for a book?
3 hours ago 78 Replies 4 Medals payton: thx to everyone who edited for me i will use your edits evey now and then
3 hours ago 17 Replies 1 Medal SaltTheLoser: How do you make edits?
5 hours ago 10 Replies 1 Medal Lexya: How do I make music with an egg and a toothpick
2 hours ago 25 Replies 3 Medals xxcoffee: who wanna edit a pic for me.even doe im ugly
5 hours ago 0 Replies 0 Medals