ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

Solve the trigonometric integral $\int\sin\left(x\right)^4dx$

Go!
Symbolic 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
Dx
|◻|
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

 Final answer to the problem

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}-\frac{3}{16}\sin\left(2x\right)+\frac{3}{8}x+C_0$
Got another answer? Verify it here!

 Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

Apply the formula: $\int\sin\left(\theta \right)^ndx$$=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)}{n}+\frac{n-1}{n}\int\sin\left(\theta \right)^{\left(n-2\right)}dx$, where $n=4$

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}+\frac{3}{4}\int\sin\left(x\right)^{2}dx$

Learn how to solve trigonometric integrals problems step by step online.

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}+\frac{3}{4}\int\sin\left(x\right)^{2}dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(x)^4)dx. Apply the formula: \int\sin\left(\theta \right)^ndx=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)}{n}+\frac{n-1}{n}\int\sin\left(\theta \right)^{\left(n-2\right)}dx, where n=4. Multiply the single term \frac{3}{4} by each term of the polynomial \left(\frac{1}{2}x-\frac{1}{4}\sin\left(2x\right)\right). The integral \frac{3}{4}\int\sin\left(x\right)^{2}dx results in: \frac{1}{2}\cdot \frac{3}{4}x-\frac{1}{4}\cdot \frac{3}{4}\sin\left(2x\right). Gather the results of all integrals.

 Final answer to the problem

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}-\frac{3}{16}\sin\left(2x\right)+\frac{3}{8}x+C_0$

 Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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
|◻|
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

 Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.