Please answer part a in latex that i can copy and past in jupyterhub

The Planck theory of thermal radiation tells us that in the (angular) frequency interval to +d, a black body of unit area radiates electromagnetically an amount of thermal energy per second equal to I()d, where I()=42c2n(ehkBBT1)3. Here is Planck's constant over 2,c is the speed of light, and kB is Boltzmann's constant. (a) Show that the total energy per unit area radiated by a black body is W=42c2n3kB4T40ex1x3dx. Hint: Refer to section 5.8 of Newman's book and use a change of variables. You can write your solution in a Markdown box using LateX, or you can upload your answer to the Jupyterhub as a file (e.g. scanning in your answer). (b) Write a program to evaluate the integral in this expression. (c) Even before Planck gave his theory of thermal radiation around the turn of the 20th century, it was known that the total energy W given off by a black body per unit area per second followed Stefan's law: W=T4, where is the Stefan-Boltzmann constant. Use your value for the integral above to compute a value for the Stefan- Boltzmann constant (in SI units) to three significant figures. Check your result against the known value, which you can find in books or online. You should get good agreement. [20 points]