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Popular Calculus Problems

integral of 2x(4x^2-10)^2	\int\:2x(4x^{2}-10)^{2}dx
derivative of f(x)=-3x^2+5x+2	derivative\:f(x)=-3x^{2}+5x+2
integral from 2 to 3 of x/((x^2-3)^2)	\int\:_{2}^{3}\frac{x}{(x^{2}-3)^{2}}dx
integral of 4/((x^2-4))	\int\:\frac{4}{(x^{2}-4)}dx
xy^'-y=2x^2+2x+2	xy^{\prime\:}-y=2x^{2}+2x+2
derivative of x+e^x	\frac{d}{dx}(x+e^{x})
(\partial)/(\partial x)(y/(2x^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{2x^{2}})
derivative of 1/(arccos(3x))	\frac{d}{dx}(\frac{1}{\arccos(3x)})
integral of x^2cos(y)	\int\:x^{2}\cos(y)dy
integral of 2/y	\int\:\frac{2}{y}dy
derivative of 3x^5sqrt(x)	derivative\:3x^{5}\sqrt{x}
d/(dt)(2+4t)	\frac{d}{dt}(2+4t)
8sqrt(xy)(dy)/(dx)=1	8\sqrt{xy}\frac{dy}{dx}=1
integral of cos^3(x/(16))	\int\:\cos^{3}(\frac{x}{16})dx
sum from n=0 to infinity of e^{-a*n}	\sum\:_{n=0}^{\infty\:}e^{-a\cdot\:n}
integral from 2 to 3 of 20x	\int\:_{2}^{3}20xdx
area f(x)=x^2-4,g(x)=0	area\:f(x)=x^{2}-4,g(x)=0
derivative of 1/2 (2-x^2)^{-1/2}	derivative\:\frac{1}{2}(2-x^{2})^{-\frac{1}{2}}
(\partial)/(\partial x)(e^{2x}cos(x^2y))	\frac{\partial\:}{\partial\:x}(e^{2x}\cos(x^{2}y))
limit as x approaches-5+of 2/(x^2-25)	\lim\:_{x\to\:-5+}(\frac{2}{x^{2}-25})
derivative of x^3(x-4^2)	\frac{d}{dx}(x^{3}(x-4)^{2})
derivative of f(x)=(2x)/((x^2-x))	derivative\:f(x)=\frac{2x}{(x^{2}-x)}
derivative of 1/(3sqrt(x))	\frac{d}{dx}(\frac{1}{3\sqrt{x}})
integral of 7^x-sec^2(x)	\int\:7^{x}-\sec^{2}(x)dx
integral of sin((pix)/a)	\int\:\sin(\frac{πx}{a})dx
derivative of (x^2-6x-1/((x-3)^2))	\frac{d}{dx}(\frac{x^{2}-6x-1}{(x-3)^{2}})
y^{''}+8y^'+25y=0,y(0)=-3,y^'(0)=1	y^{\prime\:\prime\:}+8y^{\prime\:}+25y=0,y(0)=-3,y^{\prime\:}(0)=1
integral from-5 to 3 of sqrt(\|x\|+1)	\int\:_{-5}^{3}\sqrt{\left\|x\right\|+1}dx
sum from n=2 to infinity of 3/(6^n)	\sum\:_{n=2}^{\infty\:}\frac{3}{6^{n}}
limit as x approaches 0 of e^xcos(5x)	\lim\:_{x\to\:0}(e^{x}\cos(5x))
81y^{''}+72y^'+16y=0,y(0)=5,y^'(0)=-1	81y^{\prime\:\prime\:}+72y^{\prime\:}+16y=0,y(0)=5,y^{\prime\:}(0)=-1
laplacetransform e^{(2t)/1}	laplacetransform\:e^{\frac{2t}{1}}
inverse oflaplace (6s^2)/(s^2(s^2+16))	inverselaplace\:\frac{6s^{2}}{s^{2}(s^{2}+16)}
(\partial)/(\partial x)((3x-5)/(2x+4))	\frac{\partial\:}{\partial\:x}(\frac{3x-5}{2x+4})
limit as x approaches 0+of (14x^3+15x)/x	\lim\:_{x\to\:0+}(\frac{14x^{3}+15x}{x})
integral of-4sin(4t)	\int\:-4\sin(4t)dt
(dy)/(dx)=6e^x	\frac{dy}{dx}=6e^{x}
(\partial)/(\partial t)(-2sqrt(s^2+t^2))	\frac{\partial\:}{\partial\:t}(-2\sqrt{s^{2}+t^{2}})
derivative of 6x+2	\frac{d}{dx}(6x+2)
integral of 4sin^{-3/2}(x)cos^3(x)	\int\:4\sin^{-\frac{3}{2}}(x)\cos^{3}(x)dx
integral from 0 to 7 of sqrt(x+9)	\int\:_{0}^{7}\sqrt{x+9}dx
f(x)=sqrt(3)x	f(x)=\sqrt{3}x
tangent of x^4+2x^2-x	tangent\:x^{4}+2x^{2}-x
(dy)/(dx)=(1+y^2)/(3+7x)	\frac{dy}{dx}=\frac{1+y^{2}}{3+7x}
derivative of 125e^{5x}	\frac{d}{dx}(125e^{5x})
derivative of-7/x	derivative\:-\frac{7}{x}
derivative of sqrt(x^2-7x)	derivative\:\sqrt{x^{2}-7x}
tangent of y=sqrt(x),(1,1)	tangent\:y=\sqrt{x},(1,1)
derivative of (sin(x)/(x+1))	\frac{d}{dx}(\frac{\sin(x)}{x+1})
limit as x approaches 0 of ((2x^2-3x))/x	\lim\:_{x\to\:0}(\frac{(2x^{2}-3x)}{x})
laplacetransform 3(5e^{-5.06s})+3(2.26*5e^{-5.06s})	laplacetransform\:3\cdot\:(5e^{-5.06s})+3\cdot\:(2.26\cdot\:5e^{-5.06s})
integral of ((9sqrt(4-x^2)))/2	\int\:\frac{(9\sqrt{4-x^{2}})}{2}dx
(\partial)/(\partial x)(sin(2x+y))	\frac{\partial\:}{\partial\:x}(\sin(2x+y))
derivative of-(x-3^2)	\frac{d}{dx}(-(x-3)^{2})
derivative of-xcsc^2(x)	\frac{d}{dx}(-x\csc^{2}(x))
sum from n=1 to infinity of 3/(e^n)	\sum\:_{n=1}^{\infty\:}\frac{3}{e^{n}}
integral of 1/(x^2+2x+10)	\int\:\frac{1}{x^{2}+2x+10}dx
integral of x(2+x^2)^3	\int\:x(2+x^{2})^{3}dx
inverse oflaplace (-a-b)/((s+1))	inverselaplace\:\frac{-a-b}{(s+1)}
derivative of 2/3 x^{3/2}	derivative\:\frac{2}{3}x^{\frac{3}{2}}
inverse oflaplace 3/(s(s+2))	inverselaplace\:\frac{3}{s(s+2)}
integral of 1/(8sqrt(x))	\int\:\frac{1}{8\sqrt{x}}dx
y^{''}-5y^'+6y=36t	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=36t
x derivative of [ln(y)]=1	x\frac{d}{dx}[\ln(y)]=1
area y=x,y=4x,y=-x+2	area\:y=x,y=4x,y=-x+2
integral of 6sin(3x)	\int\:6\sin(3x)dx
simplify (x^2-3)/((x-1)^2+(x-1)^2)	simplify\:\frac{x^{2}-3}{(x-1)^{2}+(x-1)^{2}}
integral from 1 to 4 of 1/(9+(x-1)^2)	\int\:_{1}^{4}\frac{1}{9+(x-1)^{2}}dx
derivative of 24sqrt(x)-4x	\frac{d}{dx}(24\sqrt{x}-4x)
derivative of \sqrt[7]{x}-5/x	\frac{d}{dx}(\sqrt[7]{x}-\frac{5}{x})
derivative of (8sqrt(x))/x	derivative\:\frac{8\sqrt{x}}{x}
integral of (x^3)/2+1/(2x^3)	\int\:\frac{x^{3}}{2}+\frac{1}{2x^{3}}dx
integral from 0 to pi/2 of (cos(x))	\int\:_{0}^{\frac{π}{2}}(\cos(x))dx
integral of 11/12 x^2+1/12 x	\int\:\frac{11}{12}x^{2}+\frac{1}{12}xdx
d/(dt)(sin(t))	\frac{d}{dt}(\sin(t))
integral of (1-1/x)	\int\:(1-\frac{1}{x})dx
(\partial)/(\partial t)(e^{-2t})	\frac{\partial\:}{\partial\:t}(e^{-2t})
integral of x^4-6x	\int\:x^{4}-6xdx
derivative of 6e^xt+xt	\frac{d}{dx}(6e^{x}t+xt)
area 7x,2x^2	area\:7x,2x^{2}
derivative of ln({f}(x)(x))	\frac{d}{dx}(\ln({f}(x))(x))
y^'=(sec(y))/((x-1)^2)	y^{\prime\:}=\frac{\sec(y)}{(x-1)^{2}}
(dy}{dx}-\frac{2y)/x+x^2y^2=0	\frac{dy}{dx}-\frac{2y}{x}+x^{2}y^{2}=0
derivative of tan(2xsin(2x))	\frac{d}{dx}(\tan(2x)\sin(2x))
tangent of f(x)=19x-x^2,\at x=9	tangent\:f(x)=19x-x^{2},\at\:x=9
limit as x approaches 2-of-x+10	\lim\:_{x\to\:2-}(-x+10)
limit as x approaches 0 of (x^4-x^3)/3	\lim\:_{x\to\:0}(\frac{x^{4}-x^{3}}{3})
integral of (sin(x)e^{i*t})	\int\:(\sin(x)e^{i\cdot\:t})dt
derivative of ln(xln(x)ln(x))	\frac{d}{dx}(\ln(x)\ln(x)\ln(x))
derivative of x^{1/7}	derivative\:x^{\frac{1}{7}}
d/(dy)((x+y)e^y)	\frac{d}{dy}((x+y)e^{y})
derivative of (4+8xcos(1-x))	\frac{d}{dx}((4+8x)\cos(1-x))
derivative of (x+1(x^3+3))	\frac{d}{dx}((x+1)(x^{3}+3))
integral of (4x+1)/(2x^2+x-3)	\int\:\frac{4x+1}{2x^{2}+x-3}dx
inverse oflaplace 4/(s(s^2+4))	inverselaplace\:\frac{4}{s(s^{2}+4)}
derivative of-(x^2+2x/((x+1)^2))	\frac{d}{dx}(-\frac{x^{2}+2x}{(x+1)^{2}})
(\partial)/(\partial x)((x^2+tx)/(sin(tx)))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}+tx}{\sin(tx)})
tangent of f(x)= x/(x^2+9),\at x=0	tangent\:f(x)=\frac{x}{x^{2}+9},\at\:x=0
derivative of y=sqrt(3x^2-4)	derivative\:y=\sqrt{3x^{2}-4}
derivative of ln(x^2-8)	\frac{d}{dx}(\ln(x^{2}-8))

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