Math Question and Answers


Question and Answers Forum

All Questions Topic List
Integration Questions
Previous in All Question Next in All Question
Previous in Integration Next in Integration
Question Number 158674 by cortano last updated on 07/Nov/21

Commented by tounghoungko last updated on 07/Nov/21

$I_{1} = \int \frac{d x}{\sqrt[3]{x} + \sqrt[4]{x}}; x = r^{12}$ $I_{1} = \int \frac{12 r^{11}}{r^{4} + r^{3}} d r = \int \frac{12 r^{8}}{r + 1} d r$
Commented by tounghoungko last updated on 07/Nov/21

$I_{2} = \int \frac{\ln (1 + \sqrt[6]{x})}{\sqrt[3]{x} + \sqrt{x}} d x$ $l e t x = h^{6} \Rightarrow d x = 6 h^{5} d h$ $I_{2} = \int \frac{\ln (1 + h)}{h^{2} + h^{3}} (6 h^{5}) d h$ $I_{2} = \int \frac{\ln (1 + h)}{1 + h} (6 h^{3} d h)$ $l e t u = \ln (1 + h) \Rightarrow d u = \frac{d h}{1 + h}$ $\Rightarrow h = e^{u} - 1$ $I_{2} = 6 \int {(e^{u} - 1)}^{3} u d u$ $I_{2} = 6 \int u (e^{3 u} - 3 e^{2 u} + 3 e^{u} - 1) d u$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum