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Popular Calculus Problems

(2x)dx+(2y-4x^2y^{-1})dy=0	(2x)dx+(2y-4x^{2}y^{-1})dy=0
derivative of ln\|x^2-1\|	\frac{d}{dx}(\ln\left\|x^{2}-1\right\|)
integral of u/((u^2+1)(1-2u)(1+2u))	\int\:\frac{u}{(u^{2}+1)(1-2u)(1+2u)}du
integral of (7x+3)/(x^2-2x+1)	\int\:\frac{7x+3}{x^{2}-2x+1}dx
inverse oflaplace (e^{2s})/(s^3)	inverselaplace\:\frac{e^{2s}}{s^{3}}
(\partial)/(\partial x)(xye^{sin(pixy)})	\frac{\partial\:}{\partial\:x}(xye^{\sin(πxy)})
limit as x approaches-3 of (5-x) 4/3	\lim\:_{x\to\:-3}((5-x)\frac{4}{3})
integral of 5/(1+9x^2)	\int\:\frac{5}{1+9x^{2}}dx
integral of y^2cosh(7y)	\int\:y^{2}\cosh(7y)dy
limit as x approaches 0 of x/(4^x-2^x)	\lim\:_{x\to\:0}(\frac{x}{4^{x}-2^{x}})
integral from 0 to 7 of (8t)/((t-8)^2)	\int\:_{0}^{7}\frac{8t}{(t-8)^{2}}dt
limit as x approaches 0-of x*sin(1/x)	\lim\:_{x\to\:0-}(x\cdot\:\sin(\frac{1}{x}))
d/(dt)(-e^{-t})	\frac{d}{dt}(-e^{-t})
derivative of x^27^x	\frac{d}{dx}(x^{2}7^{x})
integral of (5x)/((x^2+2)^2)	\int\:\frac{5x}{(x^{2}+2)^{2}}dx
integral from-1 to 1 of (2sqrt(1-x^2))^2	\int\:_{-1}^{1}(2\sqrt{1-x^{2}})^{2}dx
integral of (2/(\sqrt[3]{x)})	\int\:(\frac{2}{\sqrt[3]{x}})dx
derivative of 3sec(3x)	derivative\:3\sec(3x)
integral of 2520x\sqrt[3]{5+3x}	\int\:2520x\sqrt[3]{5+3x}dx
limit as x approaches infinity of-2x^3	\lim\:_{x\to\:\infty\:}(-2x^{3})
laplacetransform cos(t-pi/2)\H(t-pi/2)	laplacetransform\:\cos(t-\frac{π}{2})\H(t-\frac{π}{2})
derivative of xsqrt(a+bx)	derivative\:x\sqrt{a+bx}
integral of (ln(6x))/(x^4)	\int\:\frac{\ln(6x)}{x^{4}}dx
integral from 1 to sqrt(2 of)x	\int\:_{1}^{\sqrt{2}}xdx
(\partial)/(\partial z)(arctan(y/x))	\frac{\partial\:}{\partial\:z}(\arctan(\frac{y}{x}))
integral of 1/(x^2*sqrt(9-x^2))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{9-x^{2}}}dx
integral of (x^2-x+10)/((x+2)(x^2+4))	\int\:\frac{x^{2}-x+10}{(x+2)(x^{2}+4)}dx
(\partial)/(\partial x)(2x^3+x^2y^3-3y^2)	\frac{\partial\:}{\partial\:x}(2x^{3}+x^{2}y^{3}-3y^{2})
(dy)/(dx)=(cos(14x))/(e^{14y)}	\frac{dy}{dx}=\frac{\cos(14x)}{e^{14y}}
sum from n=0 to infinity of 3(-0.1)^n	\sum\:_{n=0}^{\infty\:}3(-0.1)^{n}
integral of arctan(u)	\int\:\arctan(u)du
integral from-4 to 4 of 4(16-x^2)	\int\:_{-4}^{4}4(16-x^{2})dx
derivative of 2x^3-5	derivative\:2x^{3}-5
limit as x approaches-1-of 1/(x-1)+e^x	\lim\:_{x\to\:-1-}(\frac{1}{x-1}+e^{x})
d/(dt)(3t)	\frac{d}{dt}(3t)
integral of ((x^2+2x+1))/((x+3))	\int\:\frac{(x^{2}+2x+1)}{(x+3)}dx
(dy)/(dt)=y^2-4	\frac{dy}{dt}=y^{2}-4
derivative of f(x)=sqrt(7x+1)	derivative\:f(x)=\sqrt{7x+1}
y^'= x/(1+2y),y(-1)=0	y^{\prime\:}=\frac{x}{1+2y},y(-1)=0
derivative of f(x)= pi/3	derivative\:f(x)=\frac{π}{3}
integral of 3/((2x-1))	\int\:\frac{3}{(2x-1)}dx
limit as (x,y) approaches (0,0) of e^{xy}	\lim\:_{(x,y)\to\:(0,0)}(e^{xy})
derivative of (17-(13-2x^4^7)^3)	\frac{d}{dx}((17-(13-2x^{4})^{7})^{3})
(\partial)/(\partial x)(2x^2ln(3xy^2+4y))	\frac{\partial\:}{\partial\:x}(2x^{2}\ln(3xy^{2}+4y))
derivative of xe^{-x/2}	\frac{d}{dx}(xe^{-\frac{x}{2}})
integral from 0 to 5 of pi(sqrt(5x))^2	\int\:_{0}^{5}π(\sqrt{5x})^{2}dx
integral from 1 to 3 of (2x+1)	\int\:_{1}^{3}(2x+1)dx
(\partial)/(\partial x)((x^2y^2)/(x^4+y^4))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}y^{2}}{x^{4}+y^{4}})
integral of 1/(sec^4(1/4 β))	\int\:\frac{1}{\sec^{4}(\frac{1}{4}β)}dβ
integral of 6*sqrt(x+4)	\int\:6\cdot\:\sqrt{x+4}dx
(\partial)/(\partial x)(sin(x+2y+3z))	\frac{\partial\:}{\partial\:x}(\sin(x+2y+3z))
derivative of f(x)=(4x)/(3x^2+1)	derivative\:f(x)=\frac{4x}{3x^{2}+1}
limit as x approaches 4 of 7/((x-4))	\lim\:_{x\to\:4}(\frac{7}{(x-4)})
(\partial)/(\partial x)(yln(xy))	\frac{\partial\:}{\partial\:x}(y\ln(xy))
limit as x approaches 2 of 6/((x-2)^3)	\lim\:_{x\to\:2}(\frac{6}{(x-2)^{3}})
implicit (dy)/(dx),7x+4y=8	implicit\:\frac{dy}{dx},7x+4y=8
integral of (5e^x-2/x)	\int\:(5e^{x}-\frac{2}{x})dx
area y=x^2,y=5x	area\:y=x^{2},y=5x
derivative of ln(2x-3)	\frac{d}{dx}(\ln(2x-3))
inverse oflaplace ((5e^{-s}))/(s+1)	inverselaplace\:\frac{(5e^{-s})}{s+1}
tangent of f(x)=sqrt(3x+7),\at a=6	tangent\:f(x)=\sqrt{3x+7},\at\:a=6
d/(dy)(x/((x+y)^2))	\frac{d}{dy}(\frac{x}{(x+y)^{2}})
derivative of (5-x/x)	\frac{d}{dx}(\frac{5-x}{x})
integral of x^3-1/(x^2)-x^{2/3}	\int\:x^{3}-\frac{1}{x^{2}}-x^{\frac{2}{3}}dx
limit as x approaches infinity of 5x^2	\lim\:_{x\to\:\infty\:}(5x^{2})
integral from 1 to 4 of x-1	\int\:_{1}^{4}x-1dx
derivative of (7^{10x+1})	\frac{d}{dx}((7)^{10x+1})
derivative of 10xe^{-5x}	\frac{d}{dx}(10xe^{-5x})
integral from 0 to pi/8 of cos^4(x)	\int\:_{0}^{\frac{π}{8}}\cos^{4}(x)dx
derivative of x^2*x^{-1}	\frac{d}{dx}(x^{2}\cdot\:x^{-1})
integral of (2x+1)/(x^2+2x+37)	\int\:\frac{2x+1}{x^{2}+2x+37}dx
(\partial)/(\partial z)(x^2yz)	\frac{\partial\:}{\partial\:z}(x^{2}yz)
derivative of sin(x*sin(x))	\frac{d}{dx}(\sin(x)\cdot\:\sin(x))
integral from-9 to 9 of sqrt(81-x^2)	\int\:_{-9}^{9}\sqrt{81-x^{2}}dx
ty^'-2y=t^5sin(2t)-t^3+4t^4	ty^{\prime\:}-2y=t^{5}\sin(2t)-t^{3}+4t^{4}
tangent of f(x)=(12x)/(x^2-4),\at x=4	tangent\:f(x)=\frac{12x}{x^{2}-4},\at\:x=4
limit as h approaches 0 of (-8+h)/h	\lim\:_{h\to\:0}(\frac{-8+h}{h})
(e^{-1/(x^2)})^'	(e^{-\frac{1}{x^{2}}})^{\prime\:}
integral of (e^x)/(sqrt(e^{2x)+1)}	\int\:\frac{e^{x}}{\sqrt{e^{2x}+1}}dx
integral from 2 to 3 of 5/(sqrt(3-x))	\int\:_{2}^{3}\frac{5}{\sqrt{3-x}}dx
(\partial)/(\partial x)(x^2*y^3)	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:y^{3})
integral of x(x+a)(x+b)	\int\:x(x+a)(x+b)dx
y^{''}+20y^'+500=12	y^{\prime\:\prime\:}+20y^{\prime\:}+500=12
integral of 1/(sqrt(x-1)+\sqrt{1+x)}	\int\:\frac{1}{\sqrt{x-1}+\sqrt{1+x}}dx
y^'=2+sqrt(y-2x+3)	y^{\prime\:}=2+\sqrt{y-2x+3}
derivative of 2/((x+3^3))	\frac{d}{dx}(\frac{2}{(x+3)^{3}})
laplacetransform y	laplacetransform\:y
derivative of sqrt(2)	derivative\:\sqrt{2}
derivative of-csc(x)cot(x)	derivative\:-\csc(x)\cot(x)
10x+(dy)/(dx)=0	10x+\frac{dy}{dx}=0
integral of (x^2+4)/(x-1)	\int\:\frac{x^{2}+4}{x-1}dx
(\partial)/(\partial y)(e^{xyz})	\frac{\partial\:}{\partial\:y}(e^{xyz})
derivative of sin(4x^2)	derivative\:\sin(4x^{2})
dr=e(rsin(θ)dθ-cos(θ)dr)	dr=e(r\sin(θ)dθ-\cos(θ)dr)
integral of y-x/(y^2)sin(x/y)	\int\:y-\frac{x}{y^{2}}\sin(\frac{x}{y})dy
(\partial)/(\partial y)(1+x^4+y^3)	\frac{\partial\:}{\partial\:y}(1+x^{4}+y^{3})
integral of (3x+2)^{3/2}	\int\:(3x+2)^{\frac{3}{2}}dx
(\partial)/(\partial x)((x^2+y^2)^{1/2})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{\frac{1}{2}})
derivative of ((1-sec(x))/(tan(x)))	\frac{d}{dx}(\frac{(1-\sec(x))}{\tan(x)})
simplify sqrt(x)+1/(x^2)+x^3	simplify\:\sqrt{x}+\frac{1}{x^{2}}+x^{3}

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