Integration
asked Sep 12 in Other Math Topics by Iviwe

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

2 Answers

This is a little hard for me, but I'll try.

1 + 1 = 2 (x) = x = 2.
answered Sep 12 by Mathical Level 10 User (55,960 points)

Integration by parts of In(x+1)/√x+1

Let I = int {ln(x+1)/√x + 1} dx

Let I1 = int {ln(x+1)/√x} dx

Integrating by parts,

I1 = 2√x.ln(x+1) – int{2√x/(x+1)} dx

I1 = 2√x.ln(x+1) – 2.I2

where I2 = int{√x/(x+1)} dx.

Let u = √x

Then du = 1/(2√x) dx

Or, dx = 2u du

Substituting for the above into I2,

I2 = int{u/(u^2+1)} 2u.du

I2 = 2.int{u^2/(u^2+1)}.du = 2.int{(u^2+1 – 1)/(u^2+1)}.du = 2.int{1 – 1/(u^2+1)}.du

I2 = 2u – 2.arctan(u)

Hence, I1 = 2√x.ln(x+1) – 2.I2 = 2√x.ln(x+1) – 4u + 4.arctan(u)

I1 = 2√x.ln(x+1) – 4√x + 4.arctan(√x)

Hence, I = I1 + int{1} dx

I = 2√x.ln(x+1) – 4√x + 4.arctan(√x) + x

answered Sep 13 by Fermat Level 10 User (74,280 points)
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
79,115 questions
83,001 answers
1,986 comments
65,139 users