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 x*2^(-x)
-
Integral of x*sin2x
-
Integral of x^5/(x^2+1)
-
Integral of cos(3x)dx
-
Identical expressions
- (sin^ two)2xcos3xdx
- ( sinus of squared )2x co sinus of e of 3xdx
- ( sinus of to the power of two)2x co sinus of e of 3xdx
- (sin2)2xcos3xdx
- sin22xcos3xdx
- (sin²)2xcos3xdx
- (sin to the power of 2)2xcos3xdx
- sin^22xcos3xdx
Integral of (sin^2)2xcos3xdx dx
The solution
You have entered
[src]
1 / | | 2 | sin (x)*2*x*cos(3*x) dx | / 0
$$\int\limits_{0}^{1} x 2 \sin^{2}{\left(x \right)} \cos{\left(3 x \right)}\, dx$$
Integral(((sin(x)^2*2)*x)*cos(3*x), (x, 0, 1))
The answer (Indefinite)
[src]
/ | 3 5 5 4 3 2 2 3 | 2 4*cos (x) 208*cos (x) 3 2 16*x*sin (x) 16*sin (x)*cos(x) 104*cos (x)*sin (x) 8*x*cos (x)*sin (x) | sin (x)*2*x*cos(3*x) dx = C - --------- + ----------- - 2*x*sin (x) - 2*sin (x)*cos(x) + ------------ + ----------------- + ------------------- + ------------------- | 3 225 15 15 45 3 /
$$\int x 2 \sin^{2}{\left(x \right)} \cos{\left(3 x \right)}\, dx = C + \frac{16 x \sin^{5}{\left(x \right)}}{15} + \frac{8 x \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - 2 x \sin^{3}{\left(x \right)} + \frac{16 \sin^{4}{\left(x \right)} \cos{\left(x \right)}}{15} + \frac{104 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{45} - 2 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{208 \cos^{5}{\left(x \right)}}{225} - \frac{4 \cos^{3}{\left(x \right)}}{3}$$
The graph
Use the examples entering the upper and lower limits of integration.