**Hi everyone! On friday's class we learned all about the method of substitution.**

**There are 3 main steps to this method:**

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**1.**

__SUBSTITUTE:__**-you let the inner function g(x) = u**

**-differentiate that inner function and let it = du/dx**

**-we solve for du by multiplying dx to the other side (cross multiply):**

**eg.**

__du__= 3**dx**

**du = 3dx**

**-substitute u and du in original given integral.**

**2.**

__ANTIDIFFERENTIATE:__**-antidifferentiate the new integral that consist of u and du**.

**3.**

__RESUBSTITUTE:__

**-substitute g(x) the inner function in for u**

**to get your final answer, an antiderivative.**

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__REMEMBER:__It doesn't hurt to check your final answer by differentiating!!!**If it matches the given integral then your answer is right!!!**

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**The following examples we did in class will show and explain this method:**

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**1) the integral of sin (3x) dx**

**Click--> on pic so it's easier to read**

**ANSWER: -1/3 cos(3x) + C**

***DON'T FORGET + C**

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**2) the integral of 5e^5x dx**

**Click--> on pic so it's easier to read**

**ANSWER: e^5x + C**

***DON'T FORGET + C**

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**3) the integral of (x^3+2)^4 ( 3x^2) dx**

**Click--> on pic so it's easier to read**

**Answer: (x^3+2)^5 / 5 + C**

***DON'T FORGET + C.**

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**3) the integral of (x^3+2)^4 ( x^2) dx**

**- similar to question #3 but WITHOUT the 3 in front of x^**

**Click--> on pic so it's easier to read**

**Answer: (x^3+2)^5 / 15 + C**

***DON'T FORGET + C.**

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**4) the integral of (x / √x+7 ) dx**

**Click--> on pic so it's easier to read**

Answer: 2/3(x+7)^3/2 - 14(x+7)^1/2 + C

Answer: 2/3(x+7)^3/2 - 14(x+7)^1/2 + C

***DON'T FORGET + C.**

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**HOMEWORK: 7.3 Exercises --> odd #'s**

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**The next scriber is MARK =]**

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