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- Integral of d{x}:
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Integral of k
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Integral of -y
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Integral of x*e^(2*x)*dx
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Integral of (1-x^2)^(1/2)
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Identical expressions
- sin(30x+ one)^ five (cos(30x+ one)^ two)
- sinus of (30x plus 1) to the power of 5( co sinus of e of (30x plus 1) squared )
- sinus of (30x plus one) to the power of five ( co sinus of e of (30x plus one) to the power of two)
- sin(30x+1)5(cos(30x+1)2)
- sin30x+15cos30x+12
- sin(30x+1)⁵(cos(30x+1)²)
- sin(30x+1) to the power of 5(cos(30x+1) to the power of 2)
- sin30x+1^5cos30x+1^2
- sin(30x+1)^5(cos(30x+1)^2)dx
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Similar expressions
- sin(30x+1)^5(cos(30x-1)^2)
- sin(30x-1)^5(cos(30x+1)^2)
Integral of sin(30x+1)^5(cos(30x+1)^2) dx
The solution
You have entered
[src]
1 / | | 5 2 | sin (30*x + 1)*cos (30*x + 1) dx | / 0
$$\int\limits_{0}^{1} \sin^{5}{\left(30 x + 1 \right)} \cos^{2}{\left(30 x + 1 \right)}\, dx$$
Integral(sin(30*x + 1)^5*cos(30*x + 1)^2, (x, 0, 1))
The graph
The answer
[src]
7 7 5 2 3 4 3 4 5 2
4*cos (31) 4*cos (1) 2*cos (31)*sin (31) cos (31)*sin (31) cos (1)*sin (1) 2*cos (1)*sin (1)
- ---------- + --------- - ------------------- - ----------------- + --------------- + -----------------
1575 1575 225 90 90 225
$$- \frac{4 \cos^{7}{\left(31 \right)}}{1575} - \frac{2 \sin^{2}{\left(31 \right)} \cos^{5}{\left(31 \right)}}{225} - \frac{\sin^{4}{\left(31 \right)} \cos^{3}{\left(31 \right)}}{90} + \frac{4 \cos^{7}{\left(1 \right)}}{1575} + \frac{2 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{225} + \frac{\sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{90}$$
=
=
7 7 5 2 3 4 3 4 5 2
4*cos (31) 4*cos (1) 2*cos (31)*sin (31) cos (31)*sin (31) cos (1)*sin (1) 2*cos (1)*sin (1)
- ---------- + --------- - ------------------- - ----------------- + --------------- + -----------------
1575 1575 225 90 90 225
$$- \frac{4 \cos^{7}{\left(31 \right)}}{1575} - \frac{2 \sin^{2}{\left(31 \right)} \cos^{5}{\left(31 \right)}}{225} - \frac{\sin^{4}{\left(31 \right)} \cos^{3}{\left(31 \right)}}{90} + \frac{4 \cos^{7}{\left(1 \right)}}{1575} + \frac{2 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{225} + \frac{\sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{90}$$
-4*cos(31)^7/1575 + 4*cos(1)^7/1575 - 2*cos(31)^5*sin(31)^2/225 - cos(31)^3*sin(31)^4/90 + cos(1)^3*sin(1)^4/90 + 2*cos(1)^5*sin(1)^2/225
Use the examples entering the upper and lower limits of integration.