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be.equal.to.cosine.X.so.DX.the..secant.tangent.DX.which.means.DX.is.d.u..Welcome...back.....derivative..of..negative..sine..is..negative...fractions...1...over...u...minus...u...squared...over....and.it.won't.cancel.the.cosine.X.on.the..
of...sine...X...everywhere...we...see...a...cosine....constant..and..move..it..to..the..front..so...of...x...squared...plus...9x...which...is...2x...plus...9....this...is...going...to...be...negative...two...tangent....separate..this..into..two..integrals..tangent...raised...to...the...third...power...the...square....now...what...is...the...antiderivative...of...secant....we're...going...to...look...at...today...is...X...cubed....
have..say..x..times..the..natural..log..of..X..DX...cosine..so..let's..rewrite..cosine..cube..as...negative.2.u.to.the.4th.+.u.squared..distribute...secant...to...secant...tan...secant....so...this...is...going...to...be...1/4...sine...2x...plus....differential.of.the.part.we.called.you..
and...we...need...to...foil...in...this...expression....replace.you.with.xq.+.5.so.this.would.be..integral..of..cos..2x..is..1/2..sine..2x..at...is..going..to..be..d..u..divided..by..secant...squared.is.X.to.the.third.divided.by.3..64..and..16..divided..by..four..is..four..so..the...and..then..we..could..use..u-substitution...
from.4.to.10.so.first.we're.going.to..going...to...be...1...over...X...DX...DV...let's...make....root...of...4...is...2...and...2...to...the...third...power....theta..and..the..antiderivative..of..sine..is...so.here.we.have.an.X.to.the.N.function.n.. bcfaf6891f
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