In this question you will use integration by parts twice. Consider the integral

Question

In this question, you will use integration by parts twice. Consider the integral

I = ∫sin(4x)cosh(3x)dx

Think of this as s ∫uv′ dx Let u= cosh(3 x) .

Now apply integration by parts to this second integral, so consider the second integral as 

∫u2v′2dx. Note that any constants are included inside the integral. If u2= sinh(3 x) enter

(f) v′2

(h) v2 (Note: you still don’t need a constant of integration here.)

(i) Hence write the integral in the form  I=uv−u2v2+∫v2u′2dx

I= () + ∫ () dx

(j) You should notice that the integral in (i) is a multiple of the original integral, I.

Hence rearrange the equation in (i) to determine the answer to the original integral, I.

(Remember you should include a constant of integration here, +c)

I=

Answer 1

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