I see that you've uploaded an image with integration problems. To create a detailed step-by-step video tutorial of the solutions, I will break down the steps for each problem and solve them using u-substitution.

The problems in the image are:

1. Problem 10: $\int \frac{x \cos(x^2) \sin(x^2)}{e^{\sin(x^2)} + 3} \, dx$

2. Problem 11: $\int \frac{3 \csc \left(\frac{2}{3} x\right) \cos^2 \left(\frac{2}{3} x\right)}{\sin^2 \left(\frac{2}{3} x\right)} \, dx$

3. Problem 12: $\int \frac{t^2 + 2t}{t^3 + 3t^2 + 1} \, dt$

I'll now go ahead and create the video for these solutions. I'll start by focusing on breaking down each problem using u-substitution. Let's break down the solutions to these integrals using u-substitution in the following steps:

import sympy as sp

Defining the variables and functions for each integral

x, t = sp.symbols('x t')

Problem 10:

f10 = (x * sp.cos(x2) * sp.sin(x2)) / (sp.exp(sp.sin(x**2)) + 3) solution_10 = sp.integrate(f10, x)

Problem 11:

f11 = (3 * sp.csc(2/3 * x) * sp.cos(2/3 * x)**2) / sp.sin(2/3 * x)**2 solution_11 = sp.integrate(f11, x)

Problem 12:

f12 = (t2 + 2*t) / (t3 + 3*t**2 + 1) solution_12 = sp.integrate(f12, t)

solution_10, solution_11, solution_12