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Popular Calculus Problems

(\partial)/(\partial x)(ln(((2x-1))/(x-1)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{(2x-1)}{x-1}))
integral of 1/x-6/(x^2+1)	\int\:\frac{1}{x}-\frac{6}{x^{2}+1}dx
derivative of f(x)=sin(cos(x^2))	derivative\:f(x)=\sin(\cos(x^{2}))
sum from n=1 to infinity of 3n^5	\sum\:_{n=1}^{\infty\:}3n^{5}
derivative of ln(x^2+1-ln(sqrt(x+1)))	\frac{d}{dx}(\ln(x^{2}+1)-\ln(\sqrt{x+1}))
(\partial)/(\partial z)(3xsin(y-z))	\frac{\partial\:}{\partial\:z}(3x\sin(y-z))
y^{''}+5y^'-14y=e^{(4x)}	y^{\prime\:\prime\:}+5y^{\prime\:}-14y=e^{(4x)}
slope of (-1.2)(3.3)	slope\:(-1.2)(3.3)
(\partial}{\partial x}(\frac{e^x)/y)	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{y})
limit as x approaches 0 of (1+ax)^{b/x}	\lim\:_{x\to\:0}((1+ax)^{\frac{b}{x}})
derivative of (sqrt(9-x^2)/(16x))	\frac{d}{dx}(\frac{\sqrt{9-x^{2}}}{16x})
(\partial)/(\partial x)(7xsin(4x^2y))	\frac{\partial\:}{\partial\:x}(7x\sin(4x^{2}y))
integral of ((z^2+1)^2)/(sqrt(z))	\int\:\frac{(z^{2}+1)^{2}}{\sqrt{z}}dz
tangent of f(x)=x^3-3x+1,(2,3)	tangent\:f(x)=x^{3}-3x+1,(2,3)
integral of cos^3(5-x)sin(5-x)	\int\:\cos^{3}(5-x)\sin(5-x)dx
(\partial)/(\partial x)(xy-x^2)	\frac{\partial\:}{\partial\:x}(xy-x^{2})
y^'=x+y,y(0)=6	y^{\prime\:}=x+y,y(0)=6
derivative of x+3y^2	\frac{d}{dx}(x+3y^{2})
(\partial)/(\partial s)(s^2+t^2)	\frac{\partial\:}{\partial\:s}(s^{2}+t^{2})
integral from 0 to 3 of 5-x^2	\int\:_{0}^{3}5-x^{2}dx
laplacetransform 2tcos(2t)	laplacetransform\:2t\cos(2t)
derivative of 7x+6	\frac{d}{dx}(7x+6)
derivative of (1+csc(x^2)/(1-cot(x^2)))	\frac{d}{dx}(\frac{1+\csc(x^{2})}{1-\cot(x^{2})})
integral of k/(x+1)	\int\:\frac{k}{x+1}dx
integral from 0 to 5 of 12sqrt(t/(t+1))	\int\:_{0}^{5}12\sqrt{\frac{t}{t+1}}dt
integral of csc(9x)	\int\:\csc(9x)dx
integral of (3x)/(x+4)	\int\:\frac{3x}{x+4}dx
integral of sqrt(y^2+4)	\int\:\sqrt{y^{2}+4}dy
maclaurin xsin(x)	maclaurin\:x\sin(x)
(\partial)/(\partial x)(x+sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(x+\sqrt{x^{2}+y^{2}})
derivative of sqrt(4x-2)	\frac{d}{dx}(\sqrt{4x-2})
integral of (x^3+4x+3)/(x^4+5x^2+4)	\int\:\frac{x^{3}+4x+3}{x^{4}+5x^{2}+4}dx
xy(dy)/(dx)=x^2+8y^2	xy\frac{dy}{dx}=x^{2}+8y^{2}
integral of (3sec^2(x))	\int\:(3\sec^{2}(x))dx
(\partial)/(\partial y)(-3xe^{3xy})	\frac{\partial\:}{\partial\:y}(-3xe^{3xy})
limit as x approaches 8 of 1	\lim\:_{x\to\:8}(1)
derivative of-pi	\frac{d}{dx}(-π)
integral of (sec(5x)+csc(5x))^2	\int\:(\sec(5x)+\csc(5x))^{2}dx
integral of (3x^2+15x)/((x-1)^2(x+2))	\int\:\frac{3x^{2}+15x}{(x-1)^{2}(x+2)}dx
sum from n=8 to infinity of cos(1/(n^3))	\sum\:_{n=8}^{\infty\:}\cos(\frac{1}{n^{3}})
derivative of (x-2)/(3x^2e^x)	derivative\:\frac{x-2}{3x^{2}e^{x}}
(\partial)/(\partial x)(sqrt(3x+4t))	\frac{\partial\:}{\partial\:x}(\sqrt{3x+4t})
derivative of f(x)=sin(3ln(x))	derivative\:f(x)=\sin(3\ln(x))
derivative of y=sqrt(11x+\sqrt{11x+\sqrt{11x)}}	derivative\:y=\sqrt{11x+\sqrt{11x+\sqrt{11x}}}
tangent of x^2+x	tangent\:x^{2}+x
derivative of (x+1)^3(x-1)	derivative\:(x+1)^{3}(x-1)
6y^{''}-11y^'+3y=0	6y^{\prime\:\prime\:}-11y^{\prime\:}+3y=0
slope of (-1,1),(4,-2)	slope\:(-1,1),(4,-2)
integral from-1 to 5 of (x-2)^2	\int\:_{-1}^{5}(x-2)^{2}dx
limit as x approaches 6 of (x^2-1)/(x-6)	\lim\:_{x\to\:6}(\frac{x^{2}-1}{x-6})
(\partial)/(\partial x)(10y+x-z(xy-121))	\frac{\partial\:}{\partial\:x}(10y+x-z(xy-121))
integral of u/v	\int\:\frac{u}{v}dv
integral of x^2*cos(x)	\int\:x^{2}\cdot\:\cos(x)dx
integral of ((-2x-6))/(x^3-2x^2-3x)	\int\:\frac{(-2x-6)}{x^{3}-2x^{2}-3x}dx
derivative of ln(49sin(2)(x))	derivative\:\ln(49\sin(2)(x))
taylor ln(1+X)	taylor\:\ln(1+X)
integral of (3x+4)/((x^2+4)(3-x))	\int\:\frac{3x+4}{(x^{2}+4)(3-x)}dx
(\partial)/(\partial x)(e^{x-y^2})	\frac{\partial\:}{\partial\:x}(e^{x-y^{2}})
integral of sin^3(y)	\int\:\sin^{3}(y)dy
derivative of 6cos(4x)	\frac{d}{dx}(6\cos(4x))
(\partial)/(\partial z)(x^2z)	\frac{\partial\:}{\partial\:z}(x^{2}z)
integral of 24sqrt(3x+5)	\int\:24\sqrt{3x+5}dx
integral of cos^2(X)	\int\:\cos^{2}(X)dX
limit as x approaches infinity of-sin(x)	\lim\:_{x\to\:\infty\:}(-\sin(x))
xy^'+(1+x)y=e^{-x}sin(2x)	xy^{\prime\:}+(1+x)y=e^{-x}\sin(2x)
derivative of xe^{-7x}	\frac{d}{dx}(xe^{-7x})
derivative of f(x)=[(4x^2+3x)cos(x)]	derivative\:f(x)=[(4x^{2}+3x)\cos(x)]
derivative of ((4z+4))/(3z^2+3z+3)	derivative\:\frac{(4z+4)}{3z^{2}+3z+3}
(dy)/(dx)=(xy)/(x^2+4),y(0)=6	\frac{dy}{dx}=\frac{xy}{x^{2}+4},y(0)=6
area 10,x,(x^2)/(40)	area\:10,x,\frac{x^{2}}{40}
integral of 2cos(-4x)+1	\int\:2\cos(-4x)+1dx
(\partial)/(\partial x)(x^2-4xy+3y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-4xy+3y^{2})
derivative of (x^3+4e^x)	\frac{d}{dx}((x^{3}+4)e^{x})
derivative of (s^{-1/2}+2s)(7-s^{-1})	derivative\:(s^{-\frac{1}{2}}+2s)(7-s^{-1})
derivative of f(x)= 6/(5x+3)	derivative\:f(x)=\frac{6}{5x+3}
integral from 0 to 2pi of e^{ix}	\int\:_{0}^{2π}e^{ix}dx
tangent of (2x)/(x+1),\at x=1	tangent\:\frac{2x}{x+1},\at\:x=1
inverse oflaplace 1/(s^2(s^2+2s+3))	inverselaplace\:\frac{1}{s^{2}(s^{2}+2s+3)}
integral of x^6e^{-4x}	\int\:x^{6}e^{-4x}dx
integral from 0 to 1 of 6/(x^2+1)	\int\:_{0}^{1}\frac{6}{x^{2}+1}dx
integral of 1/(8x^5)	\int\:\frac{1}{8x^{5}}dx
integral of cos(x)ln(sin(x))	\int\:\cos(x)\ln(\sin(x))dx
integral of e^{x^7}	\int\:e^{x^{7}}dx
inverse oflaplace e^{-cs}	inverselaplace\:e^{-cs}
(\partial)/(\partial x)(sqrt(1-x))	\frac{\partial\:}{\partial\:x}(\sqrt{1-x})
derivative of-5e^{-x}-6e^x	\frac{d}{dx}(-5e^{-x}-6e^{x})
derivative of 4-1/(x^2)	\frac{d}{dx}(4-\frac{1}{x^{2}})
integral of arcot(x)	\int\:ar\cot(x)dx
derivative of (e/x ^x)	\frac{d}{dx}((\frac{e}{x})^{x})
limit as x approaches 0 of ((5^x-1))/x	\lim\:_{x\to\:0}(\frac{(5^{x}-1)}{x})
limit as x approaches 0 of 3^x+7	\lim\:_{x\to\:0}(3^{x}+7)
derivative of xlog_{e}(x-x)	\frac{d}{dx}(x\log_{e}(x)-x)
integral of x(x+5)^8	\int\:x(x+5)^{8}dx
(\partial)/(\partial y)(e^{-y}-2x)	\frac{\partial\:}{\partial\:y}(e^{-y}-2x)
integral of (-12x-1)sqrt(-6x^2-x+1)	\int\:(-12x-1)\sqrt{-6x^{2}-x+1}dx
integral of t/(t^4+5)	\int\:\frac{t}{t^{4}+5}dt
laplacetransform 8sin(3t)+2cos(2t)	laplacetransform\:8\sin(3t)+2\cos(2t)
integral of (e^{sin(x)})/(sec(x))	\int\:\frac{e^{\sin(x)}}{\sec(x)}dx
derivative of f(x)=(3x^3+5)(x^4-5x)	derivative\:f(x)=(3x^{3}+5)(x^{4}-5x)
integral of (x+5)/(x^3+2x^2-x-2)	\int\:\frac{x+5}{x^{3}+2x^{2}-x-2}dx

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