e^x cos x dx?

Question

Integration by parts - Step by step

Answer 1

wow
∫ e^x cos x dx = (e^x (Cos[x] + Sin[x]))/2 +c

Good Luck

Answer 2

u = cos x
du = -sin x dx
dv = e^xdx
v = e^x

int(udv) = uv-int(vdu)

int(e^x cos x dx) = -e^x cos x + int(e^x sin x dx)

do the second integral by parts.

u1 = sin x
du1 = cos x dx
dv1 = e^x dx
v1 = e^x

so we get

int(e^x cos x dx) = -e^x cos x + e^x sin x - int(e^x cos x dx)

bring last term to left hand side and we get

2int(e^x cos x dx) = -e^x cos x + e^x sin x

or int(e^x cos x dx) = -(1/2)e^x cos x + (1/2)e^x sin x

Of course, I left the constant out the whole way, so unless it is a definite integral,

int(e^x cos x dx) = -(1/2)e^x cos x + (1/2)e^x sin x + constant

Answer 3

easy problem

pl see a good website...and the text book....

a good one is http://archives.math.utk.edu/visual.calculus/4/int_by_parts.1/index.html