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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) ∫ex x dx
5) ∫ex 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
Additional explanation of the composition of funcitons:
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 ∫ew − 3 dw ?
9) What is ∫8z + 4z3 − 6z2 dz ?