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

# Trigonometric Integrals Calculator

## Get detailed solutions to your math problems with our Trigonometric Integrals step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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

###  Difficult Problems

1

Here, we show you a step-by-step solved example of trigonometric integrals. This solution was automatically generated by our smart calculator:

$\int\sin\left(x\right)^4dx$
2

Apply the formula: $\int\sin\left(\theta \right)^ndx$$=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)}{n}+\frac{n-1}{n}\int\sin\left(\theta \right)^{\left(n-2\right)}dx, where n=4 \frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}+\frac{3}{4}\int\sin\left(x\right)^{2}dx Apply the formula: \int\sin\left(\theta \right)^2dx$$=\frac{\theta }{2}-\frac{1}{4}\sin\left(2\theta \right)+C$

$\frac{3}{4}\left(\frac{x}{2}-\frac{1}{4}\sin\left(2x\right)\right)$
3

The integral $\frac{3}{4}\int\sin\left(x\right)^{2}dx$ results in: $\frac{3}{4}\left(\frac{x}{2}-\frac{1}{4}\sin\left(2x\right)\right)$

$\frac{3}{4}\left(\frac{x}{2}-\frac{1}{4}\sin\left(2x\right)\right)$
4

Gather the results of all integrals

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}+\frac{3}{4}\left(\frac{x}{2}-\frac{1}{4}\sin\left(2x\right)\right)$
5

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}+\frac{3}{4}\left(\frac{x}{2}-\frac{1}{4}\sin\left(2x\right)\right)+C_0$

Solve the product $\frac{3}{4}\left(\frac{x}{2}-\frac{1}{4}\sin\left(2x\right)\right)$

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}+\frac{3}{4}\left(\frac{x}{2}\right)+\frac{3}{4}\cdot -\frac{1}{4}\sin\left(2x\right)+C_0$

Multiply $\frac{3}{4}$ times $-\frac{1}{4}$

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

Simplify $\frac{3}{4}\left(\frac{x}{2}\right)$

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

Multiply $4$ times $2$

$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)}{4}+\frac{3x}{8}-\frac{3}{16}\sin\left(2x\right)+C_0$
6

Expand and simplify

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

##  Final answer to the problem

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

### Are you struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!