Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of -4*x*exp(-2*x)
-
Integral of (4-x^2)^(1/2)
-
Integral of 1/cos^2(x)
-
Integral of 1/(1+sin(x))
-
Identical expressions
- ((sin(4x)- one)^ five)*cos(4x)
- (( sinus of (4x) minus 1) to the power of 5) multiply by co sinus of e of (4x)
- (( sinus of (4x) minus one) to the power of five) multiply by co sinus of e of (4x)
- ((sin(4x)-1)5)*cos(4x)
- sin4x-15*cos4x
- ((sin(4x)-1)⁵)*cos(4x)
- ((sin(4x)-1)^5)cos(4x)
- ((sin(4x)-1)5)cos(4x)
- sin4x-15cos4x
- sin4x-1^5cos4x
- ((sin(4x)-1)^5)*cos(4x)dx
-
Similar expressions
- ((sin(4x)+1)^5)*cos(4x)
Integral of ((sin(4x)-1)^5)*cos(4x) dx
The solution
You have entered
[src]
1 / | | 5 | (sin(4*x) - 1) *cos(4*x) dx | / 0
$$\int\limits_{0}^{1} \left(\sin{\left(4 x \right)} - 1\right)^{5} \cos{\left(4 x \right)}\, dx$$
Integral((sin(4*x) - 1)^5*cos(4*x), (x, 0, 1))
The graph
The answer
[src]
3 5 6 2 4
5*sin (4) sin (4) sin(4) sin (4) 5*sin (4) 5*sin (4)
- --------- - ------- - ------ + ------- + --------- + ---------
6 4 4 24 8 8
$$\frac{\sin^{6}{\left(4 \right)}}{24} - \frac{\sin^{5}{\left(4 \right)}}{4} - \frac{\sin{\left(4 \right)}}{4} + \frac{5 \sin^{4}{\left(4 \right)}}{8} + \frac{5 \sin^{2}{\left(4 \right)}}{8} - \frac{5 \sin^{3}{\left(4 \right)}}{6}$$
=
=
3 5 6 2 4
5*sin (4) sin (4) sin(4) sin (4) 5*sin (4) 5*sin (4)
- --------- - ------- - ------ + ------- + --------- + ---------
6 4 4 24 8 8
$$\frac{\sin^{6}{\left(4 \right)}}{24} - \frac{\sin^{5}{\left(4 \right)}}{4} - \frac{\sin{\left(4 \right)}}{4} + \frac{5 \sin^{4}{\left(4 \right)}}{8} + \frac{5 \sin^{2}{\left(4 \right)}}{8} - \frac{5 \sin^{3}{\left(4 \right)}}{6}$$
-5*sin(4)^3/6 - sin(4)^5/4 - sin(4)/4 + sin(4)^6/24 + 5*sin(4)^2/8 + 5*sin(4)^4/8
Use the examples entering the upper and lower limits of integration.