Solutions > Derivative With Respect To (WRT) Calculator >

integral of sin^7(x)cos^4(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

implicit derivative tangent volume laplace fourier

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

∫ sin⁷(x)cos⁴(x)dx

Solution

−cos⁵(x)5 +3cos⁷(x)7 −cos⁹(x)3 +cos¹¹(x)11 +C

Show Steps

Hide Steps

Solution steps

One step at a time

∫ sin⁷(x)cos⁴(x)dx

Rewrite using trig identities

=∫ (1−cos²(x))³sin(x)cos⁴(x)dx

Apply u-substitution: ∫ −u⁴(1−u²)³du

=∫ −u⁴(1−u²)³du

Expand −u⁴(1−u²)³: −u⁴+3u⁶−3u⁸+u¹⁰

=∫ −u⁴+3u⁶−3u⁸+u¹⁰du

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

=−∫ u⁴du+∫ 3u⁶du−∫ 3u⁸du+∫ u¹⁰du

∫ u⁴du=u⁵5

∫ 3u⁶du=3u⁷7

∫ 3u⁸du=u⁹3

∫ u¹⁰du=u¹¹11

=−u⁵5 +3u⁷7 −u⁹3 +u¹¹11

Substitute back u=cos(x)

=−cos⁵(x)5 +3cos⁷(x)7 −cos⁹(x)3 +cos¹¹(x)11

Add a constant to the solution

=−cos⁵(x)5 +3cos⁷(x)7 −cos⁹(x)3 +cos¹¹(x)11 +C

Derivative With Respect To (WRT) 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

Oi, faça uma pergunta sobre ∫ sin⁷(x)cos⁴(x)dx ou escolha entre as opções abaixo

Explique como resolver integrais indefinidas

Mostrar problemas relacionados

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^7(x)cos^4(x)

Solution

Solution steps

Number Line

Graph

Symbolab for Chrome

Snip & solve on any website

integral of sin^7(x)cos^4(x)

Solution

Solution steps

Number Line

Graph