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# Integration and Differentiation Help. ¬.¬ Watch

1. Hi,

If I wanted to integrate e^3x-1 dx how would I go about it? I get confused when integrating e^of something.

Also, how would I evaluate (integral)(pi/4 to 0) sin(2x+pi/4)?? I'm slightly confused with the pi part and the bit in the bracket.

When differentiating (1-cosx)/(1+cosx) is the answer -cos2x + sin2x/sin^2x??
When integrating (5)/(2x+3)^4 dx is the answer -(5)/(6)(2x+3)^3 + c??

2. Well for the first question use the substitution u=3x. Then du/dx = 3 and therefore du/3 = dx. Substitute the dx for du/3 and the 3x for u. Now integrate with respect to u, noting that the integral of e^u is just e^u. Substitute u for 3x. You should get (1/3)*e^3x-x+c. Try this for the second integral using a different substitution.
3. Can someone please help me with the other questions please, I need someone to check if I have done them correct. Also, i'm still don't understand how to integrate (integral)(pi/4 to 0) sin(2x+pi/4). I know that the sin will be -cos?? and the 2x will be x^2??

Thanks once again!
4. (Original post by FutureMedic)
the 2x will be x^2??
no

have you seen this before?

this is the case a=2, b=pi/4

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