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Popular Calculus Problems

tangent of x^{1/3}	tangent\:x^{\frac{1}{3}}
derivative of (a-7x)(a+7x)	derivative\:(a-7x)(a+7x)
(x^3+3y)dx-xdy=0	(x^{3}+3y)dx-xdy=0
(dy)/(dx)-4y=-4y^2	\frac{dy}{dx}-4y=-4y^{2}
integral of (e^x)/((e^x-9)(e^{2x)+1)}	\int\:\frac{e^{x}}{(e^{x}-9)(e^{2x}+1)}dx
integral from 0 to infinity of 7sin^2(x)	\int\:_{0}^{\infty\:}7\sin^{2}(x)dx
derivative of 1/6	\frac{d}{dx}(\frac{1}{6})
(dc)/(dc)	\frac{dc}{dc}
integral of (x^3)/2	\int\:\frac{x^{3}}{2}dx
x^'+x+2=0	x^{\prime\:}+x+2=0
derivative of e^{-sin^2(x})	\frac{d}{dx}(e^{-\sin^{2}(x)})
derivative of tan(x)	derivative\:\tan(x)
derivative of (1+4x^2)(x-x^2)	derivative\:(1+4x^{2})(x-x^{2})
derivative of Acos(x+Bsin(x))	\frac{d}{dx}(A\cos(x)+B\sin(x))
derivative of-2/(9x^{4/3})	\frac{d}{dx}(-\frac{2}{9x^{\frac{4}{3}}})
integral from-1 to 6 of-x^2+5x+6	\int\:_{-1}^{6}-x^{2}+5x+6dx
limit as x approaches 0+of (\|8x\|)/x	\lim\:_{x\to\:0+}(\frac{\left\|8x\right\|}{x})
area y=sin^2(pix),[0,1]	area\:y=\sin^{2}(πx),[0,1]
derivative of 5/(x+4)	\frac{d}{dx}(\frac{5}{x+4})
(d^2)/(dx^2)((x^2)/(9+8x))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{9+8x})
integral from 0 to 2 of-2x^2-4	\int\:_{0}^{2}-2x^{2}-4dx
area y= 1/2 x,y= 6/x	area\:y=\frac{1}{2}x,y=\frac{6}{x}
integral of (t^3)/(1+t)	\int\:\frac{t^{3}}{1+t}dt
integral of cos^4(x)sin^5(x)	\int\:\cos^{4}(x)\sin^{5}(x)dx
2xy^'+y=6x,y(4)=23	2xy^{\prime\:}+y=6x,y(4)=23
derivative of 6x^5ln(x+x^5)	\frac{d}{dx}(6x^{5}\ln(x)+x^{5})
(dy)/(dx)=8+8y+x+xy	\frac{dy}{dx}=8+8y+x+xy
d/(dy)(x/(x^2+y^2+1))	\frac{d}{dy}(\frac{x}{x^{2}+y^{2}+1})
limit as x approaches-2 of (5x-4)/(4-x)	\lim\:_{x\to\:-2}(\frac{5x-4}{4-x})
limit as x approaches 0 of (1-cos(4x))/x	\lim\:_{x\to\:0}(\frac{1-\cos(4x)}{x})
integral of 6y-x-4	\int\:6y-x-4dy
limit as x approaches 2 of 1-x	\lim\:_{x\to\:2}(1-x)
integral from 0 to 2 of 6x^3sqrt(x^2+4)	\int\:_{0}^{2}6x^{3}\sqrt{x^{2}+4}dx
tangent of f(x)=-x^2+2x+4,\at x=4	tangent\:f(x)=-x^{2}+2x+4,\at\:x=4
integral from 0 to 1 of 1/(e^{3x)}	\int\:_{0}^{1}\frac{1}{e^{3x}}dx
derivative of e^{-ax^2}	\frac{d}{dx}(e^{-ax^{2}})
sum from n=0 to infinity of (e^n)/(pi^n)	\sum\:_{n=0}^{\infty\:}\frac{e^{n}}{π^{n}}
derivative of (2x-8^4(x^2+x+1)^5)	\frac{d}{dx}((2x-8)^{4}(x^{2}+x+1)^{5})
derivative of 3(4e^{2x}x+4e^{2x})	\frac{d}{dx}(3(4e^{2x}x+4e^{2x}))
integral of x/(10-x^2)	\int\:\frac{x}{10-x^{2}}dx
sum from n=1 to infinity of 1/((2n-1))	\sum\:_{n=1}^{\infty\:}\frac{1}{(2n-1)}
integral of 7sin^4(x)cos^2(x)	\int\:7\sin^{4}(x)\cos^{2}(x)dx
(\partial)/(\partial x)(63x^8y^6-48x^7y^5)	\frac{\partial\:}{\partial\:x}(63x^{8}y^{6}-48x^{7}y^{5})
derivative of f(x)=(x^2+1)^4	derivative\:f(x)=(x^{2}+1)^{4}
y^'=0.15ln((2000)/y)y	y^{\prime\:}=0.15\ln(\frac{2000}{y})y
integral from-2 to 2 of 4x-x^3	\int\:_{-2}^{2}4x-x^{3}dx
(dy)/(dx)=(e^x)/(7+e^x)	\frac{dy}{dx}=\frac{e^{x}}{7+e^{x}}
integral of ((1+sin(2x))^4)/(sec(2x))	\int\:\frac{(1+\sin(2x))^{4}}{\sec(2x)}dx
derivative of sqrt(3x-2)	derivative\:\sqrt{3x-2}
integral of x^6e^{2x}	\int\:x^{6}e^{2x}dx
derivative of 3/((x+1))	derivative\:\frac{3}{(x+1)}
derivative of 2*sin(2x)	\frac{d}{dx}(2\cdot\:\sin(2x))
derivative of a*cos(x)	\frac{d}{dx}(a\cdot\:\cos(x))
integral of u/2	\int\:\frac{u}{2}du
integral of t^7e^{t^4}	\int\:t^{7}e^{t^{4}}dt
integral of x^2*e^{-2x}	\int\:x^{2}\cdot\:e^{-2x}dx
integral of (3x^2-5sqrt(x))/x	\int\:\frac{3x^{2}-5\sqrt{x}}{x}dx
limit as x approaches infinity of 2+1/x	\lim\:_{x\to\:\infty\:}(2+\frac{1}{x})
derivative of y=xsin(2x)	derivative\:y=x\sin(2x)
integral of (12)/(1-cos(2x))	\int\:\frac{12}{1-\cos(2x)}dx
integral from 1 to 4 of-7sqrt(x)ln(x)	\int\:_{1}^{4}-7\sqrt{x}\ln(x)dx
integral of (4x)/((3x^2-1)^5)	\int\:\frac{4x}{(3x^{2}-1)^{5}}dx
integral of ((2x+3))/(x^2+3x)	\int\:\frac{(2x+3)}{x^{2}+3x}dx
integral of (x^2+1)^{1/2}	\int\:(x^{2}+1)^{\frac{1}{2}}dx
integral of e^{3x}sin(6x)	\int\:e^{3x}\sin(6x)dx
derivative of 250000+15000x-0.3x^3	derivative\:250000+15000x-0.3x^{3}
derivative of 2x^3-2x+1	\frac{d}{dx}(2x^{3}-2x+1)
derivative of ln(5x+ln(3x))	derivative\:\ln(5x+\ln(3x))
(\partial)/(\partial y)(2x^2+3y^2)	\frac{\partial\:}{\partial\:y}(2x^{2}+3y^{2})
derivative of 1700e^x	\frac{d}{dx}(1700e^{x})
integral of (6x^2y-3xsqrt(y))	\int\:(6x^{2}y-3x\sqrt{y})dy
integral of 3sin(2θ)	\int\:3\sin(2θ)dθ
derivative of 3x^4+9x^3+11	derivative\:3x^{4}+9x^{3}+11
integral of (x(x+1)^2)/(sqrt(x))	\int\:\frac{x(x+1)^{2}}{\sqrt{x}}dx
y^{''}-6y^'+13=0	y^{\prime\:\prime\:}-6y^{\prime\:}+13=0
slope of (-4,2),(1,-4)	slope\:(-4,2),(1,-4)
(dy)/(dx)-3y=0	\frac{dy}{dx}-3y=0
area y=3+2sqrt(x),y=(6+x)/2	area\:y=3+2\sqrt{x},y=\frac{6+x}{2}
limit as x approaches-1 of x^2+8x+8	\lim\:_{x\to\:-1}(x^{2}+8x+8)
integral of (37)/(37+e^x)	\int\:\frac{37}{37+e^{x}}dx
xy^'+y-y^2e^{2x}=0	xy^{\prime\:}+y-y^{2}e^{2x}=0
derivative of f(x)=7ln(x)	derivative\:f(x)=7\ln(x)
(dy)/(dx)+ycos(x)=7cos(x),y(0)=9	\frac{dy}{dx}+y\cos(x)=7\cos(x),y(0)=9
derivative of 2x^2-5x-3	derivative\:2x^{2}-5x-3
integral from-3 to x of (t+3)	\int\:_{-3}^{x}(t+3)dt
integral of (cos(x))/(sin^5(x))	\int\:\frac{\cos(x)}{\sin^{5}(x)}dx
slope of f(x)=(x^3-3x^2+4)/(x^2)	slope\:f(x)=\frac{x^{3}-3x^{2}+4}{x^{2}}
derivative of e^x*cos(x)	\frac{d}{dx}(e^{x}\cdot\:\cos(x))
(\partial)/(\partial x)(6xe^{x+y})	\frac{\partial\:}{\partial\:x}(6xe^{x+y})
limit as x approaches 3-of 2sqrt(3-x)	\lim\:_{x\to\:3-}(2\sqrt{3-x})
d/(dy)(-y^2)	\frac{d}{dy}(-y^{2})
integral of cos((pix)/3)	\int\:\cos(\frac{πx}{3})dx
integral of (x^4+9)/(x^3)	\int\:\frac{x^{4}+9}{x^{3}}dx
xy^'=-3y	xy^{\prime\:}=-3y
integral of arctan(x/3)	\int\:\arctan(\frac{x}{3})dx
integral of x^9sqrt(x^5+6)	\int\:x^{9}\sqrt{x^{5}+6}dx
integral of sin(x) 1/(cos(x))	\int\:\sin(x)\frac{1}{\cos(x)}dx
derivative of (3x^2-1)/(2xsqrt(x))	derivative\:\frac{3x^{2}-1}{2x\sqrt{x}}
integral of (2x)^32	\int\:(2x)^{3}2dx
limit as x approaches 2 of 1/(4-x^2)	\lim\:_{x\to\:2}(\frac{1}{4-x^{2}})

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