Use substitution to compute the following indefinite integrals.

(a) ∫ln^3 x / x dx

(b)∫sin^5 xcos xdx

(c)∫e^tan x / cos^2xdx

(d)∫e^x
sin(e^x)dx

Please show your work, thanks!

a)
u = ln(x)
du = dx / x

int(u^3 * du) =>
(1/4) * u^4 + C =>
(1/4) * ln(x)^4 + C


b)
u = sin(x)
du = cos(x) * dx

int(u^5 * du) =>
(1/6) * u^6 + C =>
(1/6) * sin(x)^6 + C


c)
u = tan(x)
du = sec(x)^2 * dx

e^(tan(x)) * dx / cos(x)^2 =>
e^(tan(x)) * sec(x)^2 * dx =>
e^(u) * du
int(e^(u) * du) =>
e^(u) + C =>
e^(tan(x)) + C


d)
My browser isn't showing me the symbol between e^(x) and sin(e^(x)). Just let e^(x) = u, then du = e^(x) * dx, and you could probably go from there.

1/4 (lnx)^4 , 1/6 (sinx)^6 , e^tanx , -cos(e^x)