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Integration and derivatives evaluated

Evaluate:
∫ sinh6 xcosh xd x

Given
?(x)= csch^-1 1 /x2
find
?'(x)

Given
?(x)=log10x
find ?'(x).

Solution Preview

1.Let A= ∫ sinh6 xcoshx dx

We 'll use integration by parts:

A = ∫ sinh(6x) coshx dx ∫ sinh(6x) (sinhx)' dx = sinh(6x) (sinhx)-∫ [sinh(6x)]' sinhx dx
= sinh(6x) (sinhx)- 6∫ cosh(6x) sinhx dx

Let B=∫ cosh(6x) sinhx dx and ...

Solution Summary

This provides several examples of integrating and derivatives.

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