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Popular Calculus Problems

area 4x^2+10,2x+7,-3,2	area\:4x^{2}+10,2x+7,-3,2
derivative of 3x^2+1/(x^2)	\frac{d}{dx}(3x^{2}+\frac{1}{x^{2}})
integral of-1/(x-4)	\int\:-\frac{1}{x-4}dx
tangent of 4x-32sqrt(x),\at x=4	tangent\:4x-32\sqrt{x},\at\:x=4
integral from-1 to 1 of x^4	\int\:_{-1}^{1}x^{4}dx
sum from n=1 to infinity of n^4(1+n^5)	\sum\:_{n=1}^{\infty\:}n^{4}(1+n^{5})
integral of (x^3)/(sqrt(x^8+25))	\int\:\frac{x^{3}}{\sqrt{x^{8}+25}}dx
derivative of (1+x^n)	\frac{d}{dx}((1+x)^{n})
integral of 1/(sqrt(4-x))	\int\:\frac{1}{\sqrt{4-x}}dx
derivative of x^4-4x^3+6x^2-36x+27	\frac{d}{dx}(x^{4}-4x^{3}+6x^{2}-36x+27)
derivative of (1+csc(x)/(1+sec(x)))	\frac{d}{dx}(\frac{1+\csc(x)}{1+\sec(x)})
tangent of (1+4x)^{3/2}	tangent\:(1+4x)^{\frac{3}{2}}
derivative of (11x/(2+x^2))	\frac{d}{dx}(\frac{11x}{2+x^{2}})
integral from 0 to 10 of 49-9.8x	\int\:_{0}^{10}49-9.8xdx
derivative of y=((x^2+4)/(x^2-4))^4	derivative\:y=(\frac{x^{2}+4}{x^{2}-4})^{4}
sum from n=1 to infinity of 1/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}}
integral from 1 to 2 of 5/(x^3+3x)	\int\:_{1}^{2}\frac{5}{x^{3}+3x}dx
integral of ((3x^5-4)^2*5x^4)	\int\:((3x^{5}-4)^{2}\cdot\:5x^{4})dx
(\partial)/(\partial x)(tan(xyz))	\frac{\partial\:}{\partial\:x}(\tan(xyz))
(\partial)/(\partial x)(x^7y^6-x^6y^5)	\frac{\partial\:}{\partial\:x}(x^{7}y^{6}-x^{6}y^{5})
integral from 0 to pi of 15sin^2(4x)	\int\:_{0}^{π}15\sin^{2}(4x)dx
integral of \sqrt[6]{u}	\int\:\sqrt[6]{u}du
integral of 3x^2e^{2x}	\int\:3x^{2}e^{2x}dx
sum from n=1 to infinity of 1/n*x^n	\sum\:_{n=1}^{\infty\:}\frac{1}{n}\cdot\:x^{n}
derivative of yx	\frac{d}{dx}(yx)
y^{''}-3y^'+2y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=0,y(0)=1,y^{\prime\:}(0)=0
tangent of y=(-6x)/(x^2+1),(1,-3)	tangent\:y=\frac{-6x}{x^{2}+1},(1,-3)
y^'=y(1-0.001y)	y^{\prime\:}=y(1-0.001y)
integral from 0 to 1 of pi(x^2)^2	\int\:_{0}^{1}π(x^{2})^{2}dx
d/(dt)(6t)	\frac{d}{dt}(6t)
tangent of f(x)= x/(x+6),\at x=1	tangent\:f(x)=\frac{x}{x+6},\at\:x=1
area f(x)=3sec(x),-pi/6 <= x<= pi/6	area\:f(x)=3\sec(x),-\frac{π}{6}\le\:x\le\:\frac{π}{6}
(dy)/(dx)=((x-3))/(y+1)	\frac{dy}{dx}=\frac{(x-3)}{y+1}
(\partial)/(\partial y)(xe^{y/z})	\frac{\partial\:}{\partial\:y}(xe^{\frac{y}{z}})
derivative of 3/(2-x)	\frac{d}{dx}(\frac{3}{2-x})
integral of sec^2(3x+5)	\int\:\sec^{2}(3x+5)dx
limit as x approaches 0 of 2+3e^{-3/x}	\lim\:_{x\to\:0}(2+3e^{-\frac{3}{x}})
derivative of 2sin(1/2 x)	\frac{d}{dx}(2\sin(\frac{1}{2}x))
integral of-2sqrt(x)	\int\:-2\sqrt{x}dx
derivative of y=e^{x^2+9x+4}	derivative\:y=e^{x^{2}+9x+4}
area y=3x^2,y=16-x^2	area\:y=3x^{2},y=16-x^{2}
integral of 2/(5xsqrt(9-49x^2))	\int\:\frac{2}{5x\sqrt{9-49x^{2}}}dx
(dx)/(dt)=sin(2t)-3x	\frac{dx}{dt}=\sin(2t)-3x
(\partial)/(\partial y)(sin(y)-xy+y^2)	\frac{\partial\:}{\partial\:y}(\sin(y)-xy+y^{2})
integral of 1/((x+2)sqrt(x^2+4x+3))	\int\:\frac{1}{(x+2)\sqrt{x^{2}+4x+3}}dx
integral of 2sin^3(xco)s^2x	\int\:2\sin^{3}(xco)s^{2}xdx
area 3x^2,6x	area\:3x^{2},6x
derivative of ln(3x^2-5x+2)	\frac{d}{dx}(\ln(3x^{2}-5x+2))
integral of (x+e^x)^2	\int\:(x+e^{x})^{2}dx
integral of 1/(sqrt(x^2-3x))	\int\:\frac{1}{\sqrt{x^{2}-3x}}dx
integral of x/((x^2+3)^{3/2)}	\int\:\frac{x}{(x^{2}+3)^{\frac{3}{2}}}dx
integral of 4csc(x)	\int\:4\csc(x)dx
inverse oflaplace 4/((s+1)^3)	inverselaplace\:\frac{4}{(s+1)^{3}}
limit as x approaches 0+of x^2*ln(x)	\lim\:_{x\to\:0+}(x^{2}\cdot\:\ln(x))
q^{''}+40q^'+4000q=0	q^{\prime\:\prime\:}+40q^{\prime\:}+4000q=0
integral of (17x-3)/(3x^2+x-2)	\int\:\frac{17x-3}{3x^{2}+x-2}dx
integral of x^2sqrt(x^3+6)	\int\:x^{2}\sqrt{x^{3}+6}dx
slope of y=x^3-9x,(1,-8)	slope\:y=x^{3}-9x,(1,-8)
integral of (5-4x^2)/(3+2x)	\int\:\frac{5-4x^{2}}{3+2x}dx
derivative of y=(e^x+e^{-x})/x	derivative\:y=\frac{e^{x}+e^{-x}}{x}
derivative of (500/(1+0.06x^2))	\frac{d}{dx}(\frac{500}{1+0.06x^{2}})
integral of 1/(x+4)	\int\:\frac{1}{x+4}dx
(\partial)/(\partial y)(3(x-y)e^{3y+5x^2})	\frac{\partial\:}{\partial\:y}(3(x-y)e^{3y+5x^{2}})
integral of (sqrt(9-x^2))/x	\int\:\frac{\sqrt{9-x^{2}}}{x}dx
integral of sqrt(x^2-8x+25)	\int\:\sqrt{x^{2}-8x+25}dx
area sqrt(4x+4),[-1,5.25]	area\:\sqrt{4x+4},[-1,5.25]
integral of (88)/(x^2-121)	\int\:\frac{88}{x^{2}-121}dx
integral of 1/(y^2-y^{-1)}	\int\:\frac{1}{y^{2}-y^{-1}}dy
integral of (sec^2(sqrt(y)))/(2sqrt(y))	\int\:\frac{\sec^{2}(\sqrt{y})}{2\sqrt{y}}dy
y^{'''}+3y^{''}-4y=e^x	y^{\prime\:\prime\:\prime\:}+3y^{\prime\:\prime\:}-4y=e^{x}
integral of (3y)/x	\int\:\frac{3y}{x}
derivative of cos(x-1+1/2 x^2)	\frac{d}{dx}(\cos(x)-1+\frac{1}{2}x^{2})
derivative of f(x)= 1/(4x^2+2x)	derivative\:f(x)=\frac{1}{4x^{2}+2x}
derivative of (x^2+2)(x-5)	derivative\:(x^{2}+2)(x-5)
(\partial)/(\partial x)((x+1)^2+y^2-1)	\frac{\partial\:}{\partial\:x}((x+1)^{2}+y^{2}-1)
limit as x approaches 2 of (x^2+2x-8)/(3x-6)	\lim\:_{x\to\:2}(\frac{x^{2}+2x-8}{3x-6})
derivative of \sqrt[3]{sin(x})	\frac{d}{dx}(\sqrt[3]{\sin(x)})
y^'+(2-x/(x-1))y=0	y^{\prime\:}+(2-\frac{x}{x-1})y=0
limit as x approaches 1 of (In(x))/(x-1)	\lim\:_{x\to\:1}(\frac{In(x)}{x-1})
tangent of y=8e^xcos(x),(0,8)	tangent\:y=8e^{x}\cos(x),(0,8)
(\partial)/(\partial y)(x^{y^2})	\frac{\partial\:}{\partial\:y}(x^{y^{2}})
integral of 1/(x^3)sqrt(1-1/(x^2))	\int\:\frac{1}{x^{3}}\sqrt{1-\frac{1}{x^{2}}}dx
derivative of \sqrt[3]{x}(sqrt(x)+3)	\frac{d}{dx}(\sqrt[3]{x}(\sqrt{x}+3))
integral from 1 to 2 of 1/x-x	\int\:_{1}^{2}\frac{1}{x}-xdx
integral of cot(y)	\int\:\cot(y)dy
limit as x approaches 0+of x(1-cos(1/x))	\lim\:_{x\to\:0+}(x(1-\cos(\frac{1}{x})))
integral of 1/(x^2*sqrt(x^2+4))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{x^{2}+4}}dx
(dx)/(dt)-5x=sin(2t),x(0)=pi	\frac{dx}{dt}-5x=\sin(2t),x(0)=π
integral of tan^5(3x)	\int\:\tan^{5}(3x)dx
integral of 4/(x^2-2x)	\int\:\frac{4}{x^{2}-2x}dx
laplacetransform 5sin(2t)	laplacetransform\:5\sin(2t)
inverse oflaplace s+6	inverselaplace\:s+6
derivative of 1/(4sqrt(x))	\frac{d}{dx}(\frac{1}{4\sqrt{x}})
integral from 1 to 2 of e^{x^2}	\int\:_{1}^{2}e^{x^{2}}dx
integral from 1 to 3 of sqrt(x)arctan(sqrt(x))	\int\:_{1}^{3}\sqrt{x}\arctan(\sqrt{x})dx
limit as x approaches-2 of-x^2+7x-5	\lim\:_{x\to\:-2}(-x^{2}+7x-5)
integral of e^{-2x}cos(2x)	\int\:e^{-2x}\cos(2x)dx
(dy)/(dx)+2xy=4	\frac{dy}{dx}+2xy=4
derivative of ln(13-x^2)	\frac{d}{dx}(\ln(13-x^{2}))
integral of (csc^2(x/2))	\int\:(\csc^{2}(\frac{x}{2}))dx

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