Question

Can someone show me how to solve this step by step using U substitution

Answer 1

u=x^2 +5

Answer 2

derrive u

Answer 3

2x=du/dx

Answer 4

solve for dx

Answer 5

2x=du times dx

Answer 6

i mean du=2xdx

Answer 7

then solve for dx

Answer 8

dx=du/2x

Answer 9

plug u and dx back into the integral

Answer 10

integral xsin(u) dx

Answer 11

plug in your info

Answer 12

for dx

Answer 13

integral xsin(u)du/2x

Answer 14

sorry hold

Answer 15

u can take out a 1/ 2x to the front

Answer 16

1/2x integral xsin (u)

Answer 17

now integrate

Answer 18

and you fet 1/2x cosx(u) +c

Answer 19

plug u back into (u)

Answer 20

not sure if this is right though

Answer 21

Hmm I don't understand why there is x and u in your integral alexis D:
I'm just a lil confused.
Lemme post some notes if it will help.
\[\Large\bf\sf \int\sin(\color{orangered}{x^2+5})(\color{royalblue}{x\;dx})\]
\[\Large\bf\sf \color{orangered}{u=x^2+5}, \qquad\qquad\qquad \color{royalblue}{\frac{1}{2}du=x\;dx}\]

Becomes:\[\Large\bf\sf \int\limits\sin(\color{orangered}{u})(\color{royalblue}{\frac{1}{2}\;du})\quad=\quad \frac{1}{2}\int\limits \sin u \;du\]