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Popular Calculus Problems

integral from 3 to 4 of 1/(sin(x))	\int\:_{3}^{4}\frac{1}{\sin(x)}dx
laplacetransform 5cos(2t)-3sin(3t)	laplacetransform\:5\cos(2t)-3\sin(3t)
y^{''}-6/x y^'+(10)/(x^2)y=0	y^{\prime\:\prime\:}-\frac{6}{x}y^{\prime\:}+\frac{10}{x^{2}}y=0
limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h	\lim\:_{h\to\:0}(\frac{\sqrt{h+5}-\sqrt{5}}{h})
tangent of y= 2/(1-3x),\at x=-1	tangent\:y=\frac{2}{1-3x},\at\:x=-1
integral of (x+8)/(x^2+9)	\int\:\frac{x+8}{x^{2}+9}dx
integral of 1/(sqrt(x^2-400))	\int\:\frac{1}{\sqrt{x^{2}-400}}dx
(\partial)/(\partial x)(2x^{8y})	\frac{\partial\:}{\partial\:x}(2x^{8y})
integral of t^4ln(t)	\int\:t^{4}\ln(t)dt
derivative of f(x)=-(11)/(s^5)	derivative\:f(x)=-\frac{11}{s^{5}}
(\partial)/(\partial x)(9e^{xy}+8)	\frac{\partial\:}{\partial\:x}(9e^{xy}+8)
integral of (x^2+5)/(x^3+4x)	\int\:\frac{x^{2}+5}{x^{3}+4x}dx
(\partial)/(\partial y)((x-y)/(y+z))	\frac{\partial\:}{\partial\:y}(\frac{x-y}{y+z})
limit as x approaches-5 of (5/x+1)/(x+5)	\lim\:_{x\to\:-5}(\frac{\frac{5}{x}+1}{x+5})
(\partial)/(\partial x)(x^{y/z})	\frac{\partial\:}{\partial\:x}(x^{\frac{y}{z}})
derivative of e^{30t}	derivative\:e^{30t}
tangent of f(x)=3x^2+2x,\at x=-2	tangent\:f(x)=3x^{2}+2x,\at\:x=-2
d/(dt)(sin(6t))	\frac{d}{dt}(\sin(6t))
integral from 3 to 8 of (sqrt(x+1))/x	\int\:_{3}^{8}\frac{\sqrt{x+1}}{x}dx
area y=3x^2,y=6-3x	area\:y=3x^{2},y=6-3x
area y=x,y=5x,y=-x+4	area\:y=x,y=5x,y=-x+4
integral of (2x+1)/(x^2+2x+17)	\int\:\frac{2x+1}{x^{2}+2x+17}dx
integral from 0 to 1 of 13cos(x^2)	\int\:_{0}^{1}13\cos(x^{2})dx
derivative of-csc(x)	derivative\:-\csc(x)
integral of (sqrt(49-x^2))/x	\int\:\frac{\sqrt{49-x^{2}}}{x}dx
derivative of (0.4x+2)(0.5x-5)	derivative\:(0.4x+2)(0.5x-5)
derivative of x^7e^{10x}	\frac{d}{dx}(x^{7}e^{10x})
derivative of (x-2^4)	\frac{d}{dx}((x-2)^{4})
y^{''}-30y^'+225y=0	y^{\prime\:\prime\:}-30y^{\prime\:}+225y=0
limit as y approaches 1/2 of (16y^2-4)^4	\lim\:_{y\to\:\frac{1}{2}}((16y^{2}-4)^{4})
limit as x approaches o of x^x	\lim\:_{x\to\:o}(x^{x})
d/(dy)(2xy^4e^y)	\frac{d}{dy}(2xy^{4}e^{y})
tangent of f(x)= 2/(3x+1),\at x=-1	tangent\:f(x)=\frac{2}{3x+1},\at\:x=-1
limit as x approaches pi/3 of 7xcos(x)	\lim\:_{x\to\:\frac{π}{3}}(7x\cos(x))
derivative of 7/(4x+1)	\frac{d}{dx}(\frac{7}{4x+1})
derivative of y=e^{3-x}	derivative\:y=e^{3-x}
6x^2+(x^3+2) derivative of y=0	6x^{2}+(x^{3}+2)\frac{d}{dx}y=0
derivative of (12/x)	\frac{d}{dx}(\frac{12}{x})
integral of (sqrt(3-x))(x)	\int\:(\sqrt{3-x})(x)dx
integral of xsqrt(x+14)	\int\:x\sqrt{x+14}dx
derivative of mx^{m+5}+6x^my^n+nx^{n+3}	\frac{d}{dx}(mx^{m+5}+6x^{m}y^{n}+nx^{n+3})
integral of ln(x)(x^2)	\int\:\ln(x)(x^{2})dx
integral of sec(2θ)	\int\:\sec(2θ)dθ
tangent of f(x)=4x^2-2x+5	tangent\:f(x)=4x^{2}-2x+5
(sec^2(x))^'	(\sec^{2}(x))^{\prime\:}
integral of (-4x^3)	\int\:(-4x^{3})dx
limit as x approaches 0+of tan^x(9x)	\lim\:_{x\to\:0+}(\tan^{x}(9x))
limit as x approaches 0 of ((x+2)/x)^2-4	\lim\:_{x\to\:0}((\frac{x+2}{x})^{2}-4)
derivative of 2^{20}	derivative\:2^{20}
integral of (10x+1)sqrt(5x^2+x)	\int\:(10x+1)\sqrt{5x^{2}+x}dx
integral of xe^{-y}	\int\:xe^{-y}dy
derivative of x^4-5sqrt(x)	\frac{d}{dx}(x^{4}-5\sqrt{x})
inverse oflaplace (e^{-2s})/(s^4)	inverselaplace\:\frac{e^{-2s}}{s^{4}}
derivative of (x^3+3(x+2))	\frac{d}{dx}((x^{3}+3)(x+2))
derivative of 50x-x^2	\frac{d}{dx}(50x-x^{2})
(dy)/(dx)=k(y-70)	\frac{dy}{dx}=k(y-70)
tangent of f(x)=3xsqrt(2-5x),\at x=-1	tangent\:f(x)=3x\sqrt{2-5x},\at\:x=-1
(\partial)/(\partial x)(-4xy)	\frac{\partial\:}{\partial\:x}(-4xy)
(\partial)/(\partial y)(3xe^{9xy})	\frac{\partial\:}{\partial\:y}(3xe^{9xy})
integral of (tan(x))/(sec(x)tan(x))	\int\:\frac{\tan(x)}{\sec(x)\tan(x)}dx
integral from 1 to 5 of (2x-1)^{5/2}	\int\:_{1}^{5}(2x-1)^{\frac{5}{2}}dx
integral of 15xe^{x^2}	\int\:15xe^{x^{2}}dx
derivative of ln((2x/(x+9)))	\frac{d}{dx}(\ln(\frac{2x}{x+9}))
limit as x approaches 0-of sqrt(x)+1	\lim\:_{x\to\:0-}(\sqrt{x}+1)
b	b
area sin(x),cos(x),0,pi	area\:\sin(x),\cos(x),0,π
integral of (2^{x+1}-5^{x-1})/(10^x)	\int\:\frac{2^{x+1}-5^{x-1}}{10^{x}}dx
area 4x,4x+1, 3/(x-1)	area\:4x,4x+1,\frac{3}{x-1}
limit as x approaches 2 of (x^3-6x^2+12x-8)/(x^4-4x^3+16x-16)	\lim\:_{x\to\:2}(\frac{x^{3}-6x^{2}+12x-8}{x^{4}-4x^{3}+16x-16})
derivative of y=x^2+2x-6	derivative\:y=x^{2}+2x-6
derivative of ae^x+be^{-9x}	\frac{d}{dx}(ae^{x}+be^{-9x})
(\partial)/(\partial v)(u*cos(v))	\frac{\partial\:}{\partial\:v}(u\cdot\:\cos(v))
integral of (x-2)^3	\int\:(x-2)^{3}dx
integral from 0 to 1 of 1/((x-1)^{1/3)}	\int\:_{0}^{1}\frac{1}{(x-1)^{\frac{1}{3}}}dx
integral of 4tan^2(x)	\int\:4\tan^{2}(x)dx
integral of sin^3(x)cos(x)	\int\:\sin^{3}(x)\cos(x)dx
integral of y/(-y-1)	\int\:\frac{y}{-y-1}dy
(2+6xy)dx+(3x^2-2y)dy=0	(2+6xy)dx+(3x^{2}-2y)dy=0
integral of (sqrt(x)-1)/x	\int\:\frac{\sqrt{x}-1}{x}dx
(\partial)/(\partial y)(x^2+y^2+10)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}+10)
tangent of sqrt(sin(7x))	tangent\:\sqrt{\sin(7x)}
derivative of 1/(2+x^2)	\frac{d}{dx}(\frac{1}{2+x^{2}})
t^2y^{''}+11ty^'+25y=0,y(1)=4,y^'(1)=9	t^{2}y^{\prime\:\prime\:}+11ty^{\prime\:}+25y=0,y(1)=4,y^{\prime\:}(1)=9
integral of 18-(54)/(15-2x)	\int\:18-\frac{54}{15-2x}dx
derivative of ((x^2-4^2)/((x^2+2)^3))	\frac{d}{dx}(\frac{(x^{2}-4)^{2}}{(x^{2}+2)^{3}})
integral of 1/(sqrt(y-1))	\int\:\frac{1}{\sqrt{y-1}}dy
limit as x approaches 1 of 1^2-3	\lim\:_{x\to\:1}(1^{2}-3)
xy^'-2y=-x^2	xy^{\prime\:}-2y=-x^{2}
integral of e^{-x^5}	\int\:e^{-x^{5}}dx
integral of 1/(t^2sqrt(16-t^2))	\int\:\frac{1}{t^{2}\sqrt{16-t^{2}}}dt
slope of y=2-x^3,(1,1)	slope\:y=2-x^{3},(1,1)
y^'=(t+y)^2-1	y^{\prime\:}=(t+y)^{2}-1
integral of (3x^3-4x^2-14x+8)/(x^2-3x+1)	\int\:\frac{3x^{3}-4x^{2}-14x+8}{x^{2}-3x+1}dx
derivative of f(x)=\|x-9\|	derivative\:f(x)=\left\|x-9\right\|
derivative of arctan(sqrt(2t))	derivative\:\arctan(\sqrt{2t})
derivative of (-u^2+5)/((u^2+5)^2)	derivative\:\frac{-u^{2}+5}{(u^{2}+5)^{2}}
integral of ln(9x+7)	\int\:\ln(9x+7)dx
derivative of f(x)=(2x^2-3)^2	derivative\:f(x)=(2x^{2}-3)^{2}
integral from 1 to 3 of (3x^2+5x-4)	\int\:_{1}^{3}(3x^{2}+5x-4)dx
inverse oflaplace s-1	inverselaplace\:s-1

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