Maths

Integration rules 1

Integration rules 2

Explain the integration by parts and solve the examples below:

1) What is ∫x cos(x) dx

2) ∫ln(x)/x² dx

3) ∫ln(x) dx 

4) ∫e^x x dx

5) ∫e^x sin(x) dx

Explain Integration by Substitution and solve the examples below:

1) ∫cos(x²) 2x dx

2) ∫cos(x²) 6x dx

3) ∫x/(x²+1) dx

4) ∫(x+1)³ dx

5) ∫(5x+2)⁷ dx

Derivative rules 1

Derivative rules 2

Derivatives: Chain rule

Derivative examples:

1) what is the derivative of sin(x)

5) What is the derivative of x²+x³ ?

8) What is the derivative of cos(x)sin(x) ?

9) What is the derivative of cos(x)/x ?

11) What is ddxsin(x²) ?

12) What is ddxsin(x²) ?

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Integration examples:

1) what is the integral of sin(x) ?

2) what is the integral of 1/x ?

3) What is ∫x³ dx ?

4) What is ∫√x dx ?

5) What is ∫√x dx ?

6) What is ∫6x² dx ?

7) What is ∫cos x + x dx ?

8) What is ∫e^w − 3 dw ?

9) What is ∫8z + 4z³ − 6z² dz ?

Explonentiation rules 1

Rules for logarithms 1