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# U-Substitution - Stewart Calculus Solution

### Overview

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This course on u-substitution in calculus aims to teach students how to solve integrals using the u-substitution method. The learning outcomes include mastering the technique of u-substitution to simplify and solve complex integrals. Students will learn to identify suitable substitutions, apply the method correctly, and evaluate the integrals effectively. The course covers a variety of integral problems involving algebraic, trigonometric, exponential, and logarithmic functions. The teaching method involves presenting various integral problems and guiding students through the process of applying u-substitution to solve them. The intended audience for this course is students studying calculus who want to enhance their problem-solving skills and deepen their understanding of integration techniques.

### Syllabus

integral of (x+1)*sqrt(2x+x^2), calculus, u substitution.
integral of e^u/(1-e^u)^2, calculus u-substitution.
Integral of (lnx)^2/x, calculus u-substitution.
Integral of sec^2x*tan^3x, calculus u-substitution.
integral of (x^2+1)(x^3+3x)^4, calculus u-substitution.
integral of e^tan(x)*sec^2(x), calculus u-substitution.
integral of sin(x)/(1+cos^2(x)), calculus u-substitution.
integral of cot(x), calculus u-substitution.
integral of 1/(sqrt(1-x^2)*sin^-1(x)), calculus u-substitution.
Integral of (1+x)/(1+x^2), calculus u-substitution.
integral of x*sqrt(x-1) from 1 to 2, calculus u-substitution.
integral of 1/(1+sqrt(x))^4, calculus u-substitution.
Sect 5.5 #86.
Sect 5.5 #89.
u substitution for integral of (3x^2+e^x)/(x^3+e^x)^4.
sect 5.5 #16, integral of e^(-5r).
sect 5.5 #59, integral of e^(1/x)/x^2 from 1 to 2, u substitution.
sect 5.5 #61, integral of an odd function from -pi/4 to pi/4.
sect 5.5 #7, integral of x*sqrt(1-x^2), u substitution.
sect 5.5 #71, integral of (e^z+1)/(e^z+z) from 0 to 1, u substitution.
sect 5.5 #15, integral of cos^3(x)*sin(x), u substitution.
sect 5.5 #13, integral of dx/(5-3x).
sect 5.5 #9, integral of (1-2x)^9.

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