derivative of sin(x)

Topic

Full pad

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

ratio test integral test comparison test limit test divergence test

See All

area

asymptotes

critical points

derivative

domain

eigenvalues

eigenvectors

expand

extreme points

factor

implicit derivative

inflection points

intercepts

inverse

laplace

inverse laplace

partial fractions

range

slope

simplify

solve for

tangent

taylor

vertex

geometric test

alternating test

telescoping test

pseries test

root test

Steps Examples

Generated by AI

∫ √x2x+3 dx

Solution

√x−√32 arctan(√23 √x)+C

Show Steps

Hide Steps

Solution steps

One step at a time

∫ √x2x+3 dx

Apply u-substitution: ∫ 2u²2u²+3 du

=∫ 2u²2u²+3 du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=2· ∫ u²2u²+3 du

Long division u²2u²+3 : 12 −32(2u²+3)

=2· ∫ 12 −32(2u²+3) du

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=2(∫ 12 du−∫ 32(2u²+3) du)

∫ 12 du=12 u

∫ 32(2u²+3) du=√32√2 arctan(√23 u)

=2(12 u−√32√2 arctan(√23 u))

Substitute back u=√x

=2(12 √x−√32√2 arctan(√23 √x))

Simplify 2(12 √x−√32√2 arctan(√23 √x)): √x−√32 arctan(√23 √x)

=√x−√32 arctan(√23 √x)

Add a constant to the solution

=√x−√32 arctan(√23 √x)+C

Series Examples

Popular topics

median calculator dot product calculator arc length calculator maclaurin series calculator z score calculator critical point calculator inequalities calculator range calculator determinant calculator second derivative calculator lcm calculator partial derivative calculator complete the square calculator distributive property calculator mixed fractions calculator Time Calculator gradient calculator triple integrals calculator partial fractions calculator indefinite integral calculator solve for x calculator double integral solver vector calculator Date Calculator vertex calculator binomial expansion calculator decimal to fraction calculator difference quotient calculator eigenvalue calculator piecewise functions calculator radius of convergence calculator roots calculator exponential function calculator interval of convergence calculator fractions divide calculator inflection point calculator expand calculator variance calculator fractions multiply calculator fourier series calculator foil calculator modulo calculator series convergence calculator linear algebra calculator

Chat with Symbo

Hi, ask a question about ∫ √x2x+3 dx or choose from the options below

Show related problems

Click to practice integration

Cooking Calculators

Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter More calculators

Fitness Calculators

BMI Calculator Calorie Calculator BMR Calculator More calculators

Notebook

View Full Notebook

−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

derivative of sin(x)

Solution

Solution steps

Number Line

Graph