Solutions > Weierstrass Substitution Calculator >

integral of sin^2(x)cos^3(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

partial fractions substitution long division trigonometric substitution by parts

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

∫ sin²(x)cos³(x)dx

Solution

sin³(x)3 −sin⁵(x)5 +C

Show Steps

Hide Steps

Solution steps

One step at a time

∫ sin²(x)cos³(x)dx

Rewrite using trig identities

=∫ (1−sin²(x))cos(x)sin²(x)dx

Apply u-substitution: ∫ u²(1−u²)du

=∫ u²(1−u²)du

Expand u²(1−u²): u²−u⁴

=∫ u²−u⁴du

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

=∫ u²du−∫ u⁴du

∫ u²du=u³3

∫ u⁴du=u⁵5

=u³3 −u⁵5

Substitute back u=sin(x)

=sin³(x)3 −sin⁵(x)5

Add a constant to the solution

=sin³(x)3 −sin⁵(x)5 +C

Weierstrass Substitution 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

Salut, poser une question sur ∫ sin²(x)cos³(x)dx ou choisissez parmi les options ci-dessous

Afficher les problèmes associés

Cliquez pour vous entrainer 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`

integral of sin^2(x)cos^3(x)

Solution

Solution steps

Number Line

Graph