CK-12-Calculus

7.1. Integration by Substitution http://www.ck12.org 7.1 Integration by Substitution Each basic rule of integration that you hav ...

http://www.ck12.org Chapter 7. Integration Techniques Learning Objectives A student will be able to: Compute by hand the integr ...

7.1. Integration by Substitution http://www.ck12.org Example 1: Evaluate∫(x+ 1 )^5 dx. Solution: Letu=x+ 1 .Thendu=d(x+ 1 ) = 1 ...

http://www.ck12.org Chapter 7. Integration Techniques Trigonometric Integrands We can apply the change of variable technique to ...

7.1. Integration by Substitution http://www.ck12.org ∫ 1 cos^23 xdx= ∫ sec^23 xdx. Substituting for the argument of the secant,u ...

http://www.ck12.org Chapter 7. Integration Techniques Using Substitution on Definite Integrals Example 6: Evaluate∫ 13 √ 2 xx− 1 ...

7.1. Integration by Substitution http://www.ck12.org Let’s try the substitution method of definite integrals with a trigonometri ...

http://www.ck12.org Chapter 7. Integration Techniques 2.∫√ 2 +xdx 3.∫ √ 21 +xdx 4.∫xx+^21 dx 5.∫e−e−x+x 2 dx 6.∫^3 √t+ 5 t dt 7. ...

7.2. Integration By Parts http://www.ck12.org 7.2 Integration By Parts Learning Objectives A student will be able to: Compute b ...

http://www.ck12.org Chapter 7. Integration Techniques Evaluate∫xsinxdx. Solution: We use the formula∫udv=uv−∫vdu. Choose u=x and ...

7.2. Integration By Parts http://www.ck12.org As you can see, this integral is worse than what we started with! This tells us th ...

http://www.ck12.org Chapter 7. Integration Techniques Solution: Here, we only have one term, lnx.We can always assume that this ...

7.2. Integration By Parts http://www.ck12.org Tabular Integration by Parts Sometimes, we need to integrate by parts several time ...

http://www.ck12.org Chapter 7. Integration Techniques ∫ excosxdx=exsinx− [ −excosx− ∫ (−cosx)(exdx) ] =exsinx−excosx− ∫ excosxdx ...

7.2. Integration By Parts http://www.ck12.org ; Math Video Tutorials by James Sousa, Integration by Parts (10:03) MEDIA Click im ...

http://www.ck12.org Chapter 7. Integration Techniques 7.3 Integration by Partial Fractions Learning Objectives A student will be ...

7.3. Integration by Partial Fractions http://www.ck12.org 2 x− 19 x^2 +x− 6 = A x+ 3 + B x− 2. Our goal at this point is to find ...

http://www.ck12.org Chapter 7. Integration Techniques For each distinct factorax+b,the right side must include a term of the fo ...

7.3. Integration by Partial Fractions http://www.ck12.org ∫ x+ 1 (x+ 2 )^2 dx= ∫( 1 x+ 2 − 1 (x+ 2 )^2 ) = ∫ 1 x+ 2 dx− ∫ 1 (x+ ...

http://www.ck12.org Chapter 7. Integration Techniques Now we have solved forA,B,andC.We use the partial fraction decomposition t ...