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*e^(x*(-2))
-
Integral of e^(-x^3)
-
Integral of -exp(-3*x)
- Integral of (xcosx)/(2+3x^3)
-
Identical expressions
- xsinx^ two / two x^2+4dx
- x sinus of x squared divide by 2x squared plus 4dx
- x sinus of x to the power of two divide by two x squared plus 4dx
- xsinx2/2x2+4dx
- xsinx²/2x²+4dx
- xsinx to the power of 2/2x to the power of 2+4dx
- xsinx^2 divide by 2x^2+4dx
-
Similar expressions
- xsinx^2/2x^2-4dx
Integral of xsinx^2/2x^2+4dx dx
The solution
You have entered
[src]
1 / | | / 2 \ | |x*sin (x) 2 | | |---------*x + 4| dx | \ 2 / | / 0
$$\int\limits_{0}^{1} \left(x^{2} \frac{x \sin^{2}{\left(x \right)}}{2} + 4\right)\, dx$$
Integral(((x*sin(x)^2)/2)*x^2 + 4, (x, 0, 1))
The answer (Indefinite)
[src]
/ | | / 2 \ 2 2 2 4 2 4 2 2 2 3 | |x*sin (x) 2 | 3*sin (x) 3*x *cos (x) x *cos (x) x *sin (x) 3*x *sin (x) x *cos(x)*sin(x) 3*x*cos(x)*sin(x) | |---------*x + 4| dx = C + 4*x - --------- - ------------ + ---------- + ---------- + ------------ - ---------------- + ----------------- | \ 2 / 16 16 16 16 16 4 8 | /
$$\int \left(x^{2} \frac{x \sin^{2}{\left(x \right)}}{2} + 4\right)\, dx = C + \frac{x^{4} \sin^{2}{\left(x \right)}}{16} + \frac{x^{4} \cos^{2}{\left(x \right)}}{16} - \frac{x^{3} \sin{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{3 x^{2} \sin^{2}{\left(x \right)}}{16} - \frac{3 x^{2} \cos^{2}{\left(x \right)}}{16} + \frac{3 x \sin{\left(x \right)} \cos{\left(x \right)}}{8} + 4 x - \frac{3 \sin^{2}{\left(x \right)}}{16}$$
The graph
The answer
[src]
2 2
cos (1) sin (1) cos(1)*sin(1)
4 - ------- + ------- + -------------
8 16 8
$$- \frac{\cos^{2}{\left(1 \right)}}{8} + \frac{\sin^{2}{\left(1 \right)}}{16} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{8} + 4$$
=
=
2 2
cos (1) sin (1) cos(1)*sin(1)
4 - ------- + ------- + -------------
8 16 8
$$- \frac{\cos^{2}{\left(1 \right)}}{8} + \frac{\sin^{2}{\left(1 \right)}}{16} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{8} + 4$$
4 - cos(1)^2/8 + sin(1)^2/16 + cos(1)*sin(1)/8
The graph
Use the examples entering the upper and lower limits of integration.