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Popular Calculus Problems

integral from 3 to 8 of 1/(x^2-1)	\int\:_{3}^{8}\frac{1}{x^{2}-1}dx
tangent of y=x^2-6	tangent\:y=x^{2}-6
limit as x approaches infinity of 0+x	\lim\:_{x\to\:\infty\:}(0+x)
d/(dc)((sin(2c))/(2-cos(2c)))	\frac{d}{dc}(\frac{\sin(2c)}{2-\cos(2c)})
integral of 3/(sqrt(1-9x^2))	\int\:\frac{3}{\sqrt{1-9x^{2}}}dx
integral of (x^2-3x-4)	\int\:(x^{2}-3x-4)dx
tangent of f(x)=sqrt(x+4),(12,4)	tangent\:f(x)=\sqrt{x+4},(12,4)
4y^{''}+6y^'-4y=0	4y^{\prime\:\prime\:}+6y^{\prime\:}-4y=0
integral of 1-cos(x)	\int\:1-\cos(x)dx
derivative of f(x)=(x^3)/(6x-3)	derivative\:f(x)=\frac{x^{3}}{6x-3}
limit as x approaches 3+of (2+x)/(3-x)	\lim\:_{x\to\:3+}(\frac{2+x}{3-x})
(dy)/(dt)=(t^2+ty+y^2)/(t^2)	\frac{dy}{dt}=\frac{t^{2}+ty+y^{2}}{t^{2}}
sum from n=0 to infinity of n(n+1)	\sum\:_{n=0}^{\infty\:}n(n+1)
integral from 4 to 9 of 1/(x^2-1)	\int\:_{4}^{9}\frac{1}{x^{2}-1}dx
integral from 0 to 1 of 4e^{7sqrt(x)}	\int\:_{0}^{1}4e^{7\sqrt{x}}dx
sqrt(1-6x^2)y^'=x	\sqrt{1-6x^{2}}y^{\prime\:}=x
area x=-2,y=x+2,y=x^2	area\:x=-2,y=x+2,y=x^{2}
integral of sqrt(8y)	\int\:\sqrt{8y}dy
sum from m=2 to infinity of 5/(6^m)	\sum\:_{m=2}^{\infty\:}\frac{5}{6^{m}}
y^'=8x^6y-y,y(1)=-4	y^{\prime\:}=8x^{6}y-y,y(1)=-4
derivative of (3sqrt(x))/x	derivative\:\frac{3\sqrt{x}}{x}
integral of 3/((z^2+4)(z+1)^2)	\int\:\frac{3}{(z^{2}+4)(z+1)^{2}}dz
integral of cos(x)sin(2x)	\int\:\cos(x)\sin(2x)dx
limit as x approaches-1 of (x^7+1)/(x+1)	\lim\:_{x\to\:-1}(\frac{x^{7}+1}{x+1})
integral of (x^6+1)e^{x^7+7x}	\int\:(x^{6}+1)e^{x^{7}+7x}dx
integral of (arcsin(2x))/(sqrt(1-4x^2))	\int\:\frac{\arcsin(2x)}{\sqrt{1-4x^{2}}}dx
tangent of f(x)=sqrt(x+5),\at x=-4	tangent\:f(x)=\sqrt{x+5},\at\:x=-4
integral of tan^2(5x)sec^4(5x)	\int\:\tan^{2}(5x)\sec^{4}(5x)dx
d/(dt)(((t+1)^2)/((t-1)^2))	\frac{d}{dt}(\frac{(t+1)^{2}}{(t-1)^{2}})
integral of sin(wt-bx)	\int\:\sin(wt-bx)dt
(\partial)/(\partial y)(sqrt(2x^2+6xy+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{2x^{2}+6xy+y^{2}})
derivative of ccos(t)+t^2sin(t)	derivative\:c\cos(t)+t^{2}\sin(t)
integral of (2+2cos(θ))^2	\int\:(2+2\cos(θ))^{2}dθ
integral of 1/(4x^2+4x+10)	\int\:\frac{1}{4x^{2}+4x+10}dx
(dy)/(dx)=(3x^2y)	\frac{dy}{dx}=(3x^{2}y)
area 4x,8x^2	area\:4x,8x^{2}
tangent of f(x)=x^2-4,\at x=-5,21	tangent\:f(x)=x^{2}-4,\at\:x=-5,21
integral of x/(3x^2+1)	\int\:\frac{x}{3x^{2}+1}dx
taylor cos(x), pi/4	taylor\:\cos(x),\frac{π}{4}
derivative of f(x)=2sec(x)-3x	derivative\:f(x)=2\sec(x)-3x
integral of sin^2(xco)s^4x	\int\:\sin^{2}(xco)s^{4}xdx
limit as x approaches 0+of sin(x)ln(3x)	\lim\:_{x\to\:0+}(\sin(x)\ln(3x))
derivative of x^2-sqrt(x)+4	derivative\:x^{2}-\sqrt{x}+4
(dx)/(dy)-xy=x^2y^3	\frac{dx}{dy}-xy=x^{2}y^{3}
limit as x approaches infinity of x^{-e}	\lim\:_{x\to\:\infty\:}(x^{-e})
tangent of f(x)=2+1/x ,(2,2.5)	tangent\:f(x)=2+\frac{1}{x},(2,2.5)
(\partial)/(\partial x)(2e^{x^6y})	\frac{\partial\:}{\partial\:x}(2e^{x^{6}y})
integral from 0 to infinity of 8e^{-x}	\int\:_{0}^{\infty\:}8e^{-x}dx
integral from 0 to 5 of 4/(x^2)	\int\:_{0}^{5}\frac{4}{x^{2}}dx
derivative of e^{-x}+e^x	\frac{d}{dx}(e^{-x}+e^{x})
sum from n=4 to infinity of 1/(n^2+n)	\sum\:_{n=4}^{\infty\:}\frac{1}{n^{2}+n}
limit as x approaches 3 of (x+2)/(x-3)	\lim\:_{x\to\:3}(\frac{x+2}{x-3})
limit as x approaches 9+of (x-9)/(\|x-9\|)	\lim\:_{x\to\:9+}(\frac{x-9}{\left\|x-9\right\|})
y^{''}+6y^'+9y=12e^{-x}	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=12e^{-x}
derivative of cos((1-e^{8x}/(1+e^{8x)}))	\frac{d}{dx}(\cos(\frac{1-e^{8x}}{1+e^{8x}}))
integral of z/(10^z)	\int\:\frac{z}{10^{z}}dz
derivative of (x^{sin(x})/(cos(x)))	\frac{d}{dx}(\frac{x^{\sin(x)}}{\cos(x)})
limit as x approaches 2+of (x-2)/(\|x-2\|)	\lim\:_{x\to\:2+}(\frac{x-2}{\left\|x-2\right\|})
xe^xln(y+1)dx+(x+1)^2(1/(y+1))dy=0	xe^{x}\ln(y+1)dx+(x+1)^{2}(\frac{1}{y+1})dy=0
integral of ((3sin^3(x)))/(cos(x))	\int\:\frac{(3\sin^{3}(x))}{\cos(x)}dx
integral of (x^3+3)^{1/4}*x^5	\int\:(x^{3}+3)^{\frac{1}{4}}\cdot\:x^{5}dx
laplacetransform te^{-3t}cos(2t)	laplacetransform\:te^{-3t}\cos(2t)
integral from 1 to infinity of 1/(4^x)	\int\:_{1}^{\infty\:}\frac{1}{4^{x}}dx
integral of 3-3x	\int\:3-3xdx
integral of xcos(2x)	\int\:x\cos(2x)dx
derivative of y=e^{x^6}	derivative\:y=e^{x^{6}}
(dy)/(dx)+1/3 y=e^xy^4	\frac{dy}{dx}+\frac{1}{3}y=e^{x}y^{4}
(\partial)/(\partial y)(ln(y^2))	\frac{\partial\:}{\partial\:y}(\ln(y^{2}))
derivative of f(x)=-1/(sqrt(x))	derivative\:f(x)=-\frac{1}{\sqrt{x}}
taylor (x+3)^{1/2}	taylor\:(x+3)^{\frac{1}{2}}
integral of cos(z/y)	\int\:\cos(\frac{z}{y})dz
tangent of f(x)=-3x^2-2x^2-1,\at x=-1	tangent\:f(x)=-3x^{2}-2x^{2}-1,\at\:x=-1
integral of (cos(x))/(5+sin(x))	\int\:\frac{\cos(x)}{5+\sin(x)}dx
derivative of sqrt(11t^2+9)	derivative\:\sqrt{11t^{2}+9}
integral from 0 to 3 of 1/(x^2-6x+5)	\int\:_{0}^{3}\frac{1}{x^{2}-6x+5}dx
derivative of (6x)/((x^2+3)^2)	derivative\:\frac{6x}{(x^{2}+3)^{2}}
derivative of y=7^{x+arccos(x)}	derivative\:y=7^{x+\arccos(x)}
area x^2-4x,2x-x^2	area\:x^{2}-4x,2x-x^{2}
(\partial)/(\partial y)(xe^{y-z^2})	\frac{\partial\:}{\partial\:y}(xe^{y-z^{2}})
derivative of ln(2+e^x)	\frac{d}{dx}(\ln(2+e^{x}))
integral from-1 to 1 of (2x)/((x+7)^2)	\int\:_{-1}^{1}\frac{2x}{(x+7)^{2}}dx
(\partial)/(\partial z)(2xyz)	\frac{\partial\:}{\partial\:z}(2xyz)
6x^2y^'=y^'+3xe^{-y}	6x^{2}y^{\prime\:}=y^{\prime\:}+3xe^{-y}
derivative of-1/2+7/5 x^3	\frac{d}{dx}(-\frac{1}{2}+\frac{7}{5}x^{3})
derivative of (x^3-2x^2+3(7x^2-4x))	\frac{d}{dx}((x^{3}-2x^{2}+3)(7x^{2}-4x))
d/(dy)(ky(1-y/N)(y/M-1))	\frac{d}{dy}(ky(1-\frac{y}{N})(\frac{y}{M}-1))
(dP)/(dt)+P=10,P(0)=4	\frac{dP}{dt}+P=10,P(0)=4
(dy)/(dx)=(-x/y)	\frac{dy}{dx}=(-\frac{x}{y})
derivative of 1/(x^{1/2)}	derivative\:\frac{1}{x^{\frac{1}{2}}}
integral of (x^2)/(36+x^2)	\int\:\frac{x^{2}}{36+x^{2}}dx
derivative of 1/(6x+7)	derivative\:\frac{1}{6x+7}
derivative of cos(xln(x))	\frac{d}{dx}(\cos(x)\ln(x))
derivative of (sin(6x^3)/(5x))	\frac{d}{dx}(\frac{\sin(6)x^{3}}{5x})
integral of x(ln(x+1))	\int\:x(\ln(x+1))dx
d/(dy)(e^{xy})	\frac{d}{dy}(e^{xy})
integral from 0 to pi/2 of 3cos^5(x)	\int\:_{0}^{\frac{π}{2}}3\cos^{5}(x)dx
derivative of x^{1/4}-4e^x	\frac{d}{dx}(x^{\frac{1}{4}}-4e^{x})
derivative of sin^7(θ)	derivative\:\sin^{7}(θ)
inverse oflaplace 6/s+16(1/(s^2+16))	inverselaplace\:\frac{6}{s}+16(\frac{1}{s^{2}+16})
(\partial)/(\partial y)(xsqrt(x^2+y^2))	\frac{\partial\:}{\partial\:y}(x\sqrt{x^{2}+y^{2}})

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