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Calculus/Basic integrals.

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Expert: - 3/9/2008


Question

calc
how do you integrate the following? please help with any that you can do. the questions are in the picture file.

Answer
Hi, Cody,

That is a lot of examples.  If you can't do any of these you are probably taking a subject that is too hard for you.  

You didn't send along any of the work you already tried to do, so I will have to assume you just don't know how to get started, and I will do that for each of them.  I will also assume you know what a 'simple substitution' is, sometimes called a 'u-substitution.'  If you don't know that much, you are in deep trouble.

1. Let  u = x^2.

2. Let  u = 3x.

3. Do long division of the top by the bottom.  You learned that in basic algebra.  You will get:

POLYNOMIAL + remainder/(x+1).

Let  u = x+1 for the remainder part.  The polynomial is routine.

4. Write cos^3(5x) = (1 - sin^2(5x)) cos(5x).
Then let  u = sin(5x)

5. Let  u = 2x - 7 and write your thing with a fractional exponent.

6. Let u = sin x

7. Let  u = 9 + x^4

8. Let  u = tan(2x)  

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

Education/Credentials
(See above.)

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