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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+4)
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Integral of sin³xcosx
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Integral of (3*x^2+14*x+13)/(x+4)
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Integral of x/((x+2)(x-1))
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Identical expressions
- (cos^ five)*(thirteen -x)
- ( co sinus of e of to the power of 5) multiply by (13 minus x)
- ( co sinus of e of to the power of five) multiply by (thirteen minus x)
- (cos5)*(13-x)
- cos5*13-x
- (cos⁵)*(13-x)
- (cos^5)(13-x)
- (cos5)(13-x)
- cos513-x
- cos^513-x
- (cos^5)*(13-x)dx
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Similar expressions
- (cos^5)*(13+x)
Integral of (cos^5)*(13-x) dx
The solution
You have entered
[src]
1 / | | 5 | cos (x)*(13 - x) dx | / 0
$$\int\limits_{0}^{1} \left(13 - x\right) \cos^{5}{\left(x \right)}\, dx$$
Integral(cos(x)^5*(13 - x), (x, 0, 1))
The answer (Indefinite)
[src]
/ | 5 3 5 3 2 5 4 2 3 | 5 149*cos (x) 26*sin (x) 13*sin (x) 52*cos (x)*sin (x) 8*x*sin (x) 8*sin (x)*cos(x) 4 4*x*cos (x)*sin (x) | cos (x)*(13 - x) dx = C + 13*sin(x) - ----------- - ---------- + ---------- - ------------------ - ----------- - ---------------- - x*cos (x)*sin(x) - ------------------- | 225 3 5 45 15 15 3 /
$$\int \left(13 - x\right) \cos^{5}{\left(x \right)}\, dx = C - \frac{8 x \sin^{5}{\left(x \right)}}{15} - \frac{4 x \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - x \sin{\left(x \right)} \cos^{4}{\left(x \right)} + \frac{13 \sin^{5}{\left(x \right)}}{5} - \frac{8 \sin^{4}{\left(x \right)} \cos{\left(x \right)}}{15} - \frac{26 \sin^{3}{\left(x \right)}}{3} - \frac{52 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{45} + 13 \sin{\left(x \right)} - \frac{149 \cos^{5}{\left(x \right)}}{225}$$
The graph
The answer
[src]
5 5 3 2 4 149 149*cos (1) 32*sin (1) 4 2 3 52*cos (1)*sin (1) 8*sin (1)*cos(1) --- - ----------- + ---------- + 12*cos (1)*sin(1) + 16*cos (1)*sin (1) - ------------------ - ---------------- 225 225 5 45 15
$$- \frac{8 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15} - \frac{52 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} - \frac{149 \cos^{5}{\left(1 \right)}}{225} + \frac{149}{225} + 12 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)} + \frac{32 \sin^{5}{\left(1 \right)}}{5} + 16 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}$$
=
=
5 5 3 2 4 149 149*cos (1) 32*sin (1) 4 2 3 52*cos (1)*sin (1) 8*sin (1)*cos(1) --- - ----------- + ---------- + 12*cos (1)*sin(1) + 16*cos (1)*sin (1) - ------------------ - ---------------- 225 225 5 45 15
$$- \frac{8 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15} - \frac{52 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} - \frac{149 \cos^{5}{\left(1 \right)}}{225} + \frac{149}{225} + 12 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)} + \frac{32 \sin^{5}{\left(1 \right)}}{5} + 16 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}$$
149/225 - 149*cos(1)^5/225 + 32*sin(1)^5/5 + 12*cos(1)^4*sin(1) + 16*cos(1)^2*sin(1)^3 - 52*cos(1)^3*sin(1)^2/45 - 8*sin(1)^4*cos(1)/15
Use the examples entering the upper and lower limits of integration.