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Popular Calculus Problems

integral from-2 to-1 of 1/x	\int\:_{-2}^{-1}\frac{1}{x}dx
integral from-1 to 1 of x^2+1	\int\:_{-1}^{1}x^{2}+1dx
tangent of f(x)=x^2-2,\at x=a	tangent\:f(x)=x^{2}-2,\at\:x=a
integral of x^2sin(2x)x	\int\:x^{2}\sin(2x)xdx
integral of (x+1)/(x^2+7x+10)	\int\:\frac{x+1}{x^{2}+7x+10}dx
integral of 12-8x+x^2	\int\:12-8x+x^{2}dx
(d^2S)/(dx^2)=S	\frac{d^{2}S}{dx^{2}}=S
limit as x approaches-infinity of-3x^3-x	\lim\:_{x\to\:-\infty\:}(-3x^{3}-x)
expand (2x-6)^4(x^2+x+1)^5	expand\:(2x-6)^{4}(x^{2}+x+1)^{5}
d/(dt)(t-t^{-1})	\frac{d}{dt}(t-t^{-1})
derivative of 2x^2+7x^2+4x	derivative\:2x^{2}+7x^{2}+4x
derivative of 7arcsin(x^4)	\frac{d}{dx}(7\arcsin(x^{4}))
area 5-x^2,4x^2	area\:5-x^{2},4x^{2}
derivative of ln(x^{-3})	\frac{d}{dx}(\ln(x^{-3}))
derivative of y= 8/(x^6)-7/x	derivative\:y=\frac{8}{x^{6}}-\frac{7}{x}
integral of 13sin^2(x)cos^2(x)	\int\:13\sin^{2}(x)\cos^{2}(x)dx
integral of 1/(x^{1/4)}	\int\:\frac{1}{x^{\frac{1}{4}}}dx
tangent of f(x)=3x^2-5x,\at x=-1	tangent\:f(x)=3x^{2}-5x,\at\:x=-1
derivative of (x-sqrt(x)/(x^{1/3)})	\frac{d}{dx}(\frac{x-\sqrt{x}}{x^{\frac{1}{3}}})
(dy)/(dx)-2y=+x^2+5	\frac{dy}{dx}-2y=+x^{2}+5
tangent of (x^2)/(x^2+7)	tangent\:\frac{x^{2}}{x^{2}+7}
derivative of (7x/(sqrt(x)))	\frac{d}{dx}(\frac{7x}{\sqrt{x}})
derivative of x+ln(x+1)	\frac{d}{dx}(x+\ln(x+1))
(1+x^4)dy+x(1+4y^2)dx=0	(1+x^{4})dy+x(1+4y^{2})dx=0
integral of 2ln(3x)	\int\:2\ln(3x)dx
derivative of sqrt(csc(5x)cot(5x))	derivative\:\sqrt{\csc(5x)\cot(5x)}
slope of 7/(sqrt(x))	slope\:\frac{7}{\sqrt{x}}
(\partial)/(\partial z)(x^2+xy+y^2+2x-y)	\frac{\partial\:}{\partial\:z}(x^{2}+xy+y^{2}+2x-y)
derivative of xln(a)	\frac{d}{dx}(x\ln(a))
derivative of 22(2e^{x^2}x^2+e^{x^2})	\frac{d}{dx}(22(2e^{x^{2}}x^{2}+e^{x^{2}}))
integral of (2sin(x)-3cos(x)+12)	\int\:(2\sin(x)-3\cos(x)+12)dx
(\partial)/(\partial x)(x-4y)	\frac{\partial\:}{\partial\:x}(x-4y)
derivative of (1+x^{-1})^2	derivative\:(1+x^{-1})^{2}
integral of 1/(x^2)sqrt(3+1/x)	\int\:\frac{1}{x^{2}}\sqrt{3+\frac{1}{x}}dx
derivative of sin(ln(2x))	\frac{d}{dx}(\sin(\ln(2x)))
integral of tsec^2(3t)	\int\:t\sec^{2}(3t)dt
(d^2)/(dx^2)(1/(2+t))	\frac{d^{2}}{dx^{2}}(\frac{1}{2+t})
integral of (e^{x^2})/(x^2)	\int\:\frac{e^{x^{2}}}{x^{2}}dx
derivative of-cos^3(x)	\frac{d}{dx}(-\cos^{3}(x))
integral from 0 to pi of 5sin^2(xco)s^4x	\int\:_{0}^{π}5\sin^{2}(xco)s^{4}xdx
limit as x approaches 2 of x^2-4x+6	\lim\:_{x\to\:2}(x^{2}-4x+6)
derivative of e^xcot(y+2ycsc(y))	\frac{d}{dx}(e^{x}\cot(y)+2y\csc(y))
integral of 1/(2(x-2))	\int\:\frac{1}{2(x-2)}dx
integral from 0 to 1 of x^2e^{x^3-1}	\int\:_{0}^{1}x^{2}e^{x^{3}-1}dx
(\partial)/(\partial x)(x^2+y^3+w^4)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{3}+w^{4})
area y=\|3x\|,y=x^2-4	area\:y=\left\|3x\right\|,y=x^{2}-4
limit as x approaches infinity of 34	\lim\:_{x\to\:\infty\:}(34)
f(x)=(2x)/(x^2+1)	f(x)=\frac{2x}{x^{2}+1}
integral of 1/(1-4x)	\int\:\frac{1}{1-4x}dx
limit as x approaches-1 of (x^2+5)/(x+6)	\lim\:_{x\to\:-1}(\frac{x^{2}+5}{x+6})
limit as x approaches-3 of x^2-13	\lim\:_{x\to\:-3}(x^{2}-13)
derivative of (x^2-8x+8e^{(9x)/8})	\frac{d}{dx}((x^{2}-8x+8)e^{\frac{9x}{8}})
taylor x^x	taylor\:x^{x}
area (3-x^2)^2,x^4	area\:(3-x^{2})^{2},x^{4}
derivative of (2x+3)^{1.4}	derivative\:(2x+3)^{1.4}
x(dy)/(dx)=-y+2x^2y	x\frac{dy}{dx}=-y+2x^{2}y
derivative of (2x^2+1)(x-3)^2	derivative\:(2x^{2}+1)(x-3)^{2}
integral of 8sin^3(x)	\int\:8\sin^{3}(x)dx
integral of cos(x)csc^2(x)	\int\:\cos(x)\csc^{2}(x)dx
4xydx+(x^2+1)dy=0	4xydx+(x^{2}+1)dy=0
inverse oflaplace ((s+1))/(s^2)	inverselaplace\:\frac{(s+1)}{s^{2}}
(\partial)/(\partial x)(8e^{x-y})	\frac{\partial\:}{\partial\:x}(8e^{x-y})
integral of sqrt(2-x-x^2)	\int\:\sqrt{2-x-x^{2}}dx
(\partial)/(\partial x)(e^{x^2+y})	\frac{\partial\:}{\partial\:x}(e^{x^{2}+y})
integral of 5sin^3(xco)s^2x	\int\:5\sin^{3}(xco)s^{2}xdx
(dy)/(dx)= y/x+csc(y/x)	\frac{dy}{dx}=\frac{y}{x}+\csc(\frac{y}{x})
derivative of-2sin(x^2)-4x^2cos(x^2)	derivative\:-2\sin(x^{2})-4x^{2}\cos(x^{2})
derivative of f(x)=(x^2+3x+1)(2x+3)	derivative\:f(x)=(x^{2}+3x+1)(2x+3)
integral of (2x)/((x-2)(x+1))	\int\:\frac{2x}{(x-2)(x+1)}dx
area y= 5/x ,y= 5/(x^2),x=4	area\:y=\frac{5}{x},y=\frac{5}{x^{2}},x=4
derivative of (10\sqrt[3]{z})/(z^2)	derivative\:\frac{10\sqrt[3]{z}}{z^{2}}
derivative of Ae^{3x}*3	\frac{d}{dx}(Ae^{3x}\cdot\:3)
inverse oflaplace (s-3)/(s^2+4s+13)	inverselaplace\:\frac{s-3}{s^{2}+4s+13}
([y-y^2])/t =y^',y(1)=2	\frac{[y-y^{2}]}{t}=y^{\prime\:},y(1)=2
limit as x approaches 0 of x(11+4/x)	\lim\:_{x\to\:0}(x(11+\frac{4}{x}))
integral of cos((npi)/2 x)	\int\:\cos(\frac{nπ}{2}x)dx
(\partial)/(\partial x)((2x)/(x^2-2x))	\frac{\partial\:}{\partial\:x}(\frac{2x}{x^{2}-2x})
limit as x approaches 1 of sin(1/x)	\lim\:_{x\to\:1}(\sin(\frac{1}{x}))
integral of (x^2*sin(x))	\int\:(x^{2}\cdot\:\sin(x))dx
derivative of x^{2/3}+y^{2/3}	\frac{d}{dx}(x^{\frac{2}{3}}+y^{\frac{2}{3}})
derivative of-tan(x^2)	\frac{d}{dx}(-\tan(x^{2}))
integral from-2 to 0 of x^2	\int\:_{-2}^{0}x^{2}dx
integral from 0 to 5 of x^2sqrt(25-x^2)	\int\:_{0}^{5}x^{2}\sqrt{25-x^{2}}dx
(\partial)/(\partial x)(ln(y/x))	\frac{\partial\:}{\partial\:x}(\ln(\frac{y}{x}))
integral of 1/(ln(x^2))	\int\:\frac{1}{\ln(x^{2})}dx
sum from n=1 to infinity of (3^n)/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{5^{n}}
integral of x(x-2)^3	\int\:x(x-2)^{3}dx
tangent of f(x)=3+4x^2-2x^3,(2,3)	tangent\:f(x)=3+4x^{2}-2x^{3},(2,3)
integral of (1-x^2)^3	\int\:(1-x^{2})^{3}dx
limit as x approaches 0 of (9+x)/(x^3)	\lim\:_{x\to\:0}(\frac{9+x}{x^{3}})
(\partial)/(\partial x)((2x^2-5x)^3(2x+1))	\frac{\partial\:}{\partial\:x}((2x^{2}-5x)^{3}(2x+1))
integral from 0 to 27 of \sqrt[3]{x}	\int\:_{0}^{27}\sqrt[3]{x}dx
limit as s approaches infinity of ct	\lim\:_{s\to\:\infty\:}(ct)
area x=sqrt(y),x=2,y=0	area\:x=\sqrt{y},x=2,y=0
(dy)/(dx)= 1/(sqrt(1-x^2))	\frac{dy}{dx}=\frac{1}{\sqrt{1-x^{2}}}
derivative of 2/(\sqrt[3]{x}+3cos(x))	\frac{d}{dx}(\frac{2}{\sqrt[3]{x}}+3\cos(x))
integral from 0 to 1 of (26)/(4y-1)	\int\:_{0}^{1}\frac{26}{4y-1}dy
integral of (sec^2(x)tan(x))	\int\:(\sec^{2}(x)\tan(x))dx
integral of x^5sqrt(12+x^6)	\int\:x^{5}\sqrt{12+x^{6}}dx
derivative of ln(sqrt((2x+1)/(x^2-2)))	derivative\:\ln(\sqrt{\frac{2x+1}{x^{2}-2}})

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