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 1/sqrt(1+u^2)
-
Integral of x*sin2x
-
Integral of (1/x^2)dx
-
Integral of -x^3
-
Identical expressions
- ((cos^ three)2x)sin2x
- (( co sinus of e of cubed )2x) sinus of 2x
- (( co sinus of e of to the power of three)2x) sinus of 2x
- ((cos3)2x)sin2x
- cos32xsin2x
- ((cos³)2x)sin2x
- ((cos to the power of 3)2x)sin2x
- cos^32xsin2x
- ((cos^3)2x)sin2xdx
Integral of ((cos^3)2x)sin2x dx
The solution
You have entered
[src]
pi -- 8 / | | 3 | cos (x)*2*x*sin(2*x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{8}} x 2 \cos^{3}{\left(x \right)} \sin{\left(2 x \right)}\, dx$$
Integral(((cos(x)^3*2)*x)*sin(2*x), (x, 0, pi/8))
The answer (Indefinite)
[src]
/ | 5 5 4 2 3 | 3 32*sin (x) 4*x*cos (x) 4*cos (x)*sin(x) 16*cos (x)*sin (x) | cos (x)*2*x*sin(2*x) dx = C + ---------- - ----------- + ---------------- + ------------------ | 75 5 5 15 /
$$\int x 2 \cos^{3}{\left(x \right)} \sin{\left(2 x \right)}\, dx = C - \frac{4 x \cos^{5}{\left(x \right)}}{5} + \frac{32 \sin^{5}{\left(x \right)}}{75} + \frac{16 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{15} + \frac{4 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{5}$$
Use the examples entering the upper and lower limits of integration.