![Could anyone explain what happens after the u substitution? Also, isn't du supposed to be 2^xln(2)dx? Or is ln and log can be used interchangeably : r/calculus Could anyone explain what happens after the u substitution? Also, isn't du supposed to be 2^xln(2)dx? Or is ln and log can be used interchangeably : r/calculus](https://preview.redd.it/jtgadnz9otb41.jpg?auto=webp&s=11840db453db00c869d4ebdf5d686a20803a1983)
Could anyone explain what happens after the u substitution? Also, isn't du supposed to be 2^xln(2)dx? Or is ln and log can be used interchangeably : r/calculus
![SOLVED: 1. Evaluate the following indefinite integral: ln 2x x6 2. Evaluate the following definite integral: 10 12x5 + 8x3 S 16x + 4 dx x6 + x4 4x2 + 2x 6 SOLVED: 1. Evaluate the following indefinite integral: ln 2x x6 2. Evaluate the following definite integral: 10 12x5 + 8x3 S 16x + 4 dx x6 + x4 4x2 + 2x 6](https://cdn.numerade.com/ask_images/29cb24eb1c194ca38f542a30bba75eb4.jpg)
SOLVED: 1. Evaluate the following indefinite integral: ln 2x x6 2. Evaluate the following definite integral: 10 12x5 + 8x3 S 16x + 4 dx x6 + x4 4x2 + 2x 6
![integration - How can you solve this definitive integral $\int_{0}^{\ln(2)} \frac{x} {1+e^{-x}} dx $ - Mathematics Stack Exchange integration - How can you solve this definitive integral $\int_{0}^{\ln(2)} \frac{x} {1+e^{-x}} dx $ - Mathematics Stack Exchange](https://i.stack.imgur.com/jaeQu.jpg)
integration - How can you solve this definitive integral $\int_{0}^{\ln(2)} \frac{x} {1+e^{-x}} dx $ - Mathematics Stack Exchange
![SOLVED: 13 Integration Techniques Define the integral Ln by Ln = z(ln 2)" dx for n = 0,1,2, Show that for n 2 1 Ln 2 (Inz)" 2L,-1, and use this relation SOLVED: 13 Integration Techniques Define the integral Ln by Ln = z(ln 2)" dx for n = 0,1,2, Show that for n 2 1 Ln 2 (Inz)" 2L,-1, and use this relation](https://cdn.numerade.com/ask_images/7a7aa8a74f0d46049bfe9aa8b9cc75b4.jpg)