👉 Try now NerdPal! Our new math app on iOS and Android
Calculators Topics Solving Methods Step Checker
Book solutions
Algebra Baldor
Go Premium Topics

Integrate $\int\sqrt{4x^2+1}dx$

Used Formulas

Go!
Math mode
Text mode
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
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Solution

Formulas

Videos

Derivatives of trigonometric functions

· Derivative of secant function
$\frac{d}{dx}\left(\sec\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\sec\left(\theta \right)\tan\left(\theta \right)$

Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Trigonometric Integrals

$\int\sec\left(\theta \right)^2dx=\tan\left(\theta \right)+C$
$\int\sec\left(\theta \right)dx=\ln\left(\sec\left(\theta \right)+\tan\left(\theta \right)\right)+C$
$\int\sec\left(\theta \right)^ndx=\frac{\sin\left(\theta \right)\sec\left(\theta \right)^{\left(n-1\right)}}{n-1}+\frac{n-2}{n-1}\int\sec\left(\theta \right)^{\left(n-2\right)}dx$

Integration Techniques

· Integration by Parts
$\int udv=uv - \int vdu$

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Constant factor Rule
$\int cxdx=c\int xdx$

Function Plot

Plotting: $\frac{1}{2}x\sqrt{4x^2+1}+\frac{1}{4}\ln\left(\sqrt{4x^2+1}+2x\right)+C_0$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

Compute the integral

$\int\sqrt{5x-3}dx$

Compute the integral

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

Compute the integral

$\int x\sqrt{x+1}dx$

Compute the integral

$\int\sqrt{x}dx$

Compute the integral

$\int\sqrt{x}\ln\left(x\right)dx$

Compute the integral

$\int\sqrt{3x+2}dx$

Compute the integral

$\int x\sqrt{x+2}dx$

Main Topic: Integrals with Radicals

Integrals with radicals are those integrals that contain a radical (square root, cubic, etc.) in the numerator or denominator of the integral.

Used Formulas

8. See formulas

Related Topics

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot password?

Supercharge your math learning



Register here if you don't have an account.
Forgot password?

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account