Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step explanation

Problem to solve:

$\int\sqrt{2w+1}dw$

Learn how to solve integrals with radicals problems step by step online.

$u=2w+1$

Learn how to solve integrals with radicals problems step by step online. Calculate the integral int((2*w+1)^0.5)dw. We can solve the integral \int\sqrt{2w+1}dw by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2w+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dw in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dw in the previous equation. Substituting u and dw in the integral and simplify.

$\frac{1}{3}\sqrt{\left(2w+1\right)^{3}}+C_0$
$\int\sqrt{2w+1}dw$