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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^2/(1+x^3)
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Integral of (4-x^2)^(1/2)
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Integral of x^2/sqrt(4-x^2)
- Integral of x^2/(x-1)
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Identical expressions
- sin^ five (x)*sin^ four (x)
- sinus of to the power of 5(x) multiply by sinus of to the power of 4(x)
- sinus of to the power of five (x) multiply by sinus of to the power of four (x)
- sin5(x)*sin4(x)
- sin5x*sin4x
- sin⁵(x)*sin⁴(x)
- sin^5(x)sin^4(x)
- sin5(x)sin4(x)
- sin5xsin4x
- sin^5xsin^4x
- sin^5(x)*sin^4(x)dx
Integral of sin^5(x)*sin^4(x) dx
The solution
You have entered
[src]
1 / | | 5 4 | sin (x)*sin (x) dx | / 0
$$\int\limits_{0}^{1} \sin^{4}{\left(x \right)} \sin^{5}{\left(x \right)}\, dx$$
Integral(sin(x)^5*sin(x)^4, (x, 0, 1))
The answer (Indefinite)
[src]
/ | 5 9 3 7 | 5 4 6*cos (x) cos (x) 4*cos (x) 4*cos (x) | sin (x)*sin (x) dx = C - cos(x) - --------- - ------- + --------- + --------- | 5 9 3 7 /
$$-{{\cos ^9x}\over{9}}+{{4\,\cos ^7x}\over{7}}-{{6\,\cos ^5x}\over{5
}}+{{4\,\cos ^3x}\over{3}}-\cos x$$
The graph
The answer
[src]
5 9 3 7 128 6*cos (1) cos (1) 4*cos (1) 4*cos (1) --- - cos(1) - --------- - ------- + --------- + --------- 315 5 9 3 7
$${{128}\over{315}}-{{35\,\cos ^91-180\,\cos ^71+378\,\cos ^51-420\,
\cos ^31+315\,\cos 1}\over{315}}$$
=
=
5 9 3 7 128 6*cos (1) cos (1) 4*cos (1) 4*cos (1) --- - cos(1) - --------- - ------- + --------- + --------- 315 5 9 3 7
$$- \cos{\left(1 \right)} - \frac{6 \cos^{5}{\left(1 \right)}}{5} - \frac{\cos^{9}{\left(1 \right)}}{9} + \frac{4 \cos^{7}{\left(1 \right)}}{7} + \frac{4 \cos^{3}{\left(1 \right)}}{3} + \frac{128}{315}$$
The graph
Use the examples entering the upper and lower limits of integration.