Friday

August 22, 2014

August 22, 2014

Posted by **kchik** on Tuesday, December 4, 2012 at 12:09am.

1) e^5t sin 3t dt

2) xe^3x dx

3) x sec^2 x dx

**anybody can help me for this question?

- calculus -
**Steve**, Tuesday, December 4, 2012 at 4:40amif we let A be our integral, we have

A = ∫e^5t sin3t dt

u=e^5t

du = 5e^5t dt

dv = sin3t dt

v = -1/3 cos3t

A = uv - ∫v du

= -1/3 e^5t cos3t + 5/3 ∫e^5t cos3t dt

u=e^5t

du = 5e^5t dt

dv = cos3t dt

v = 1/3 sin3t

A = -1/3 e^5t cos3t + 5/3(1/3 e^5t sin3t - 5/3 ∫e^5t sin3t dt)

= -1/3 e^5t cos3t + 5/9 e^5t sin3t - 25/9 A

34/9 A = 1/9 e^5t (-3cos3t + 5sin3t)

A = 1/34 e^5t (-3cos3t + 5sin3t)

-----------------------------------

A = ∫xe^3x dx

u = x

du = dx

dv = e^3x dx

v = 1/3 e^3x

A = uv - ∫v du

= 1/3 xe^3x - 1/3 ∫e^3x dx

= 1/3 xe^3x - 1/9 e^3x

= 1/9 e^3x (3x-1)

------------------------

A = ∫x sec^2 x dx

u = x

du = dx

dv = sec^2 x dx

v = tan x

A = uv - ∫v du

= x tanx - ∫tanx dx

= x tanx - ∫sinx/cosx dx

= x tanx + log cosx

**Related Questions**

Integration - Intergrate sec^3(x) dx could anybody please check this answer. ...

Calculus - Integration by Parts - Please help me solve this integration problem...

AP Calculus BC - Hi! Thank you very much for your help--- I'm not sure what the ...

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

calculus - Use integration by parts to evaluate the integral of x*sec^2(3x). My ...

Maths - Integration by Parts - Question 1 e^2x Cos(4x) dx Question 2) x ...

Calculus - How do I go about integrating sin[x^(1/3)]dx?? I tried doing ...

math - I'm trying to find the convolution f*g where f(t)=g(t)=sin(t). I set up ...

calculus - Use integration by parts to evaluate the definite integral. Intergral...

Calculus AP - Evaluate the integral interval from [0 to pi] t sin(3t)dt Use ...