Thursday

August 28, 2014

August 28, 2014

Posted by **Anonymous** on Wednesday, November 7, 2012 at 10:15am.

e^2x Cos(4x) dx

Question 2)

x sin(x) dx

Question 3)

x^2 sin(x) dx

- Maths - Integration by Parts -
**Steve**, Wednesday, November 7, 2012 at 10:31amI'll do #1, you can show us where you get stuck on the others.

Let I = ∫e^2x cos4x dx

u=cos 4x

du = -4sin4x dx

dv = e^2x dx

v = 1/2 e^2x

I = uv - ∫v du

= 1/2 e^2x cos4x - ∫-2e^2x sin4x dx

Now do it again, letting u = sin4x

I = 1/2 e^2x cos4x + (e^2x sin4x - ∫4e^2x cos4x dx)

= 1/2 e^2x cos4x + e^2x sin4x - 4I

5I = 1/2 e^2x cos4x + e^2x sin4x

I = 1/10 e^2x (cos4x + 2sin4x)

**Related Questions**

Integral - That's the same as the integral of sin^2 x dx. Use integration by ...

TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...

tigonometry - expres the following as sums and differences of sines or cosines ...

Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...

algebra - Can someone please help me do this problem? That would be great! ...

maths 2 - The original question I had was write arcsin4 in the form a+ib. I ...

Geometry One multiple choice question! - Write the ratios for sin A and cos A. {...

trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...

Math - Calculus - The identity below is significant because it relates 3 ...

Calculus Problem - I need to find the integral of e^(2x)sin(3x) I used ...