For each of the following integrals indicate whether integration by substitution

Question

For each of the following integrals indicate whether integration by substitution or integration of parts is more appropriate, or if neither method is appropriate. Do not evaluate the integrals.
1. xsinx
2. X^2/1+x^3
3.x^2e^x^3
4.x^2cos(x^3)
5. 1/sqrt(5x+1) For each of the following integrals indicate whether integration by substitution or integration of parts is more appropriate, or if neither method is appropriate. Do not evaluate the integrals.
1. xsinx
2. X^2/1+x^3
3.x^2e^x^3
4.x^2cos(x^3)
5. 1/sqrt(5x+1)
1. xsinx
2. X^2/1+x^3
3.x^2e^x^3
4.x^2cos(x^3)
5. 1/sqrt(5x+1)

Explanation / Answer

1. For this we need to apply integration by parts since we cannot use integration by substitution here.

2. In this the most appropriate way to solve this problem is integarte by using substitution. Since if you take denominator as u.. the du is 3 x^2 , that can be replaced in the integral. We can easily solve this... But in integral by parts.. it is some what difficult to solve.

3.in this problem also integral by substitution is the best way to solve.. by taking u as x^3 and du will be 3x^2...

4. As like in problem 3... This problm also follows same rules

5.in this problem Also the most appropriate way is solving using integral substitution.... Let taking u= 5x+1.. du =dx.. substitute in integral.. you can easily solve this also using integration using substitution... Hence integration by substitution is most appropriate...

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.