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Popular Calculus Problems

integral of (6+sqrt(x)+x)/x	\int\:\frac{6+\sqrt{x}+x}{x}dx
integral from 1 to 2 of (2-x)	\int\:_{1}^{2}(2-x)dx
integral of sin(pix)-cos(pix)	\int\:\sin(πx)-\cos(πx)dx
y^{1/2}((dy)/(dx))+y^{3/2}=1	y^{\frac{1}{2}}(\frac{dy}{dx})+y^{\frac{3}{2}}=1
derivative of (x^2+2x-5)/((x+1)^2)	derivative\:\frac{x^{2}+2x-5}{(x+1)^{2}}
f(x)=x-sin(x)	f(x)=x-\sin(x)
derivative of (4x^2/(e^{2x)sinh(2x)})	\frac{d}{dx}(\frac{4x^{2}}{e^{2x}\sinh(2x)})
derivative of (-4+x^2^{-1})	\frac{d}{dx}((-4+x^{2})^{-1})
derivative of (sqrt(x)/2-2/(sqrt(x)))	\frac{d}{dx}(\frac{\sqrt{x}}{2}-\frac{2}{\sqrt{x}})
integral of (x+pi)cos(nx)	\int\:(x+π)\cos(nx)dx
y^{''}+2y^'+y=6x*e^{-x}	y^{\prime\:\prime\:}+2\cdot\:y^{\prime\:}+y=6\cdot\:x\cdot\:e^{-x}
integral of tan^2(4x)sec^4(4x)	\int\:\tan^{2}(4x)\sec^{4}(4x)dx
tangent of 2sqrt(x)(1.2)	tangent\:2\sqrt{x}(1.2)
integral of sin^5(12x)	\int\:\sin^{5}(12x)dx
integral from 1 to 3 of 1/(sqrt(x)(1+x))	\int\:_{1}^{3}\frac{1}{\sqrt{x}(1+x)}dx
limit as x approaches 0+of x^{x^2}	\lim\:_{x\to\:0+}(x^{x^{2}})
integral from 0 to infinity of x/(x^2+1)	\int\:_{0}^{\infty\:}\frac{x}{x^{2}+1}dx
integral of e^{15x}(15)	\int\:e^{15x}(15)dx
limit as x approaches 4 of (x-4)/(x-2)	\lim\:_{x\to\:4}(\frac{x-4}{x-2})
area f(x)=cos(x),g(x)=-cos(x)+2	area\:f(x)=\cos(x),g(x)=-\cos(x)+2
slope of (-1.4)(3.12)	slope\:(-1.4)(3.12)
tangent of y=(-x^2+10x-21)^3	tangent\:y=(-x^{2}+10x-21)^{3}
derivative of (3x+2/(cos(x)))	\frac{d}{dx}(\frac{3x+2}{\cos(x)})
derivative of e^x-e^{xcos(x})	\frac{d}{dx}(e^{x}-e^{x\cos(x)})
integral from 0 to 3 of 4/(5x^2+6x+1)	\int\:_{0}^{3}\frac{4}{5x^{2}+6x+1}dx
integral from 0 to 1 of (x^3)/(x^4-1)	\int\:_{0}^{1}\frac{x^{3}}{x^{4}-1}dx
derivative of 9x+2	\frac{d}{dx}(9x+2)
y(1-t)dt+t^2(1-t)dy=0	y(1-t)dt+t^{2}(1-t)dy=0
derivative of-(2x/((x^2+1)^2))	\frac{d}{dx}(-\frac{2x}{(x^{2}+1)^{2}})
tangent of f(x)=4x^2-3x,\at x=-1	tangent\:f(x)=4x^{2}-3x,\at\:x=-1
limit as x approaches 2 of x^2+2x-7	\lim\:_{x\to\:2}(x^{2}+2x-7)
(\partial)/(\partial y)(sin(2y))	\frac{\partial\:}{\partial\:y}(\sin(2y))
integral from 0 to 3 of (2t)/((t-4)^2)	\int\:_{0}^{3}\frac{2t}{(t-4)^{2}}dt
derivative of (x^2-3x+2)/(-x^2-4x+4)	derivative\:\frac{x^{2}-3x+2}{-x^{2}-4x+4}
(\partial)/(\partial x)(y^4sin(5x))	\frac{\partial\:}{\partial\:x}(y^{4}\sin(5x))
inverse oflaplace 1/(s^2+9)	inverselaplace\:\frac{1}{s^{2}+9}
derivative of 1/(sqrt(8)+\sqrt[3]{9})	\frac{d}{dx}(\frac{1}{\sqrt{8}}+\sqrt[3]{9})
(\partial)/(\partial y)(y/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{y}{x+y})
derivative of f(x)=(14x-x^2)^3	derivative\:f(x)=(14x-x^{2})^{3}
integral of cos^2(x)sec^2(x)	\int\:\cos^{2}(x)\sec^{2}(x)dx
sum from n=0 to infinity of 1/(5n)	\sum\:_{n=0}^{\infty\:}\frac{1}{5n}
integral of sqrt((1-x)/(1+x))*1/(x^2)	\int\:\sqrt{\frac{1-x}{1+x}}\cdot\:\frac{1}{x^{2}}dx
integral from t to 0 of 1/(1+x^2)	\int\:_{t}^{0}\frac{1}{1+x^{2}}dx
derivative of f(x)=(40)/(0.01x^2+1)	derivative\:f(x)=\frac{40}{0.01x^{2}+1}
derivative of sqrt(3x+3)	\frac{d}{dx}(\sqrt{3x+3})
integral of xcos(x)-xsin(x)	\int\:x\cos(x)-x\sin(x)dx
integral of (4x^2)/(x^2+9)	\int\:\frac{4x^{2}}{x^{2}+9}dx
integral of e^{-st}sin(t)	\int\:e^{-st}\sin(t)dt
f(x)=sqrt(16-x^2)	f(x)=\sqrt{16-x^{2}}
integral from 1 to infinity of 1/(9x+2)	\int\:_{1}^{\infty\:}\frac{1}{9x+2}dx
taylor (x-3)e^x	taylor\:(x-3)e^{x}
implicit (d^2y)/(dx^2),y=\sqrt[7]{x}	implicit\:\frac{d^{2}y}{dx^{2}},y=\sqrt[7]{x}
integral of tan(x)+2cot(x)	\int\:\tan(x)+2\cot(x)dx
integral of (sec(7x))/7	\int\:\frac{\sec(7x)}{7}dx
integral of 1/(100x-x^2)	\int\:\frac{1}{100x-x^{2}}dx
integral of (5x^3-7x^2+3x+4)	\int\:(5x^{3}-7x^{2}+3x+4)dx
tangent of y=x^2+5	tangent\:y=x^{2}+5
derivative of-cos(3x)3	derivative\:-\cos(3x)3
derivative of (x^2-1/(4-x^2))	\frac{d}{dx}(\frac{x^{2}-1}{4-x^{2}})
integral of 7/(x(x^4+2))	\int\:\frac{7}{x(x^{4}+2)}dx
(ln(x))^x	(\ln(x))^{x}
integral of sqrt(4t^2+9t^4)	\int\:\sqrt{4t^{2}+9t^{4}}dt
(dy)/(dx)+cos(x)y=cos(x)	\frac{dy}{dx}+\cos(x)y=\cos(x)
integral of x/(x^2-x-2)	\int\:\frac{x}{x^{2}-x-2}dx
integral of 4x(x^3-1/4)	\int\:4x(x^{3}-\frac{1}{4})dx
derivative of f(x)=sqrt(1-2x)	derivative\:f(x)=\sqrt{1-2x}
derivative of (x^4)/4	derivative\:\frac{x^{4}}{4}
(y-2x-1)dx+(x+y-4)dy=0	(y-2x-1)dx+(x+y-4)dy=0
limit as n approaches infinity of 4^n	\lim\:_{n\to\:\infty\:}(4^{n})
area x=-2,x=3,y=2x^2+10,y=0	area\:x=-2,x=3,y=2x^{2}+10,y=0
tangent of f(x)=9e^xcos(x),\at x=0	tangent\:f(x)=9e^{x}\cos(x),\at\:x=0
(\partial)/(\partial v)(4ucos(v))	\frac{\partial\:}{\partial\:v}(4u\cos(v))
(\partial)/(\partial x)(1/(1+e^{-x)})	\frac{\partial\:}{\partial\:x}(\frac{1}{1+e^{-x}})
integral of (sin(3x))/3	\int\:\frac{\sin(3x)}{3}dx
integral of (-x)/(1+x)	\int\:\frac{-x}{1+x}dx
derivative of sqrt(x)e^{-x^2}	\frac{d}{dx}(\sqrt{x}e^{-x^{2}})
integral from 0 to 2 of x	\int\:_{0}^{2}xdx
f(x)=10^{sqrt(x)}	f(x)=10^{\sqrt{x}}
integral of sin(10t)	\int\:\sin(10t)dt
derivative of (2x+1)/(x+2)	derivative\:\frac{2x+1}{x+2}
taylor (7-3x^2)^{1/2},0	taylor\:(7-3x^{2})^{\frac{1}{2}},0
integral of 1/2+3/4 x^2-4/5 x^3	\int\:\frac{1}{2}+\frac{3}{4}x^{2}-\frac{4}{5}x^{3}dx
laplacetransform 3e^{(-2t)}	laplacetransform\:3e^{(-2t)}
area y= 4/x ,y=8x,y= 1/8 x	area\:y=\frac{4}{x},y=8x,y=\frac{1}{8}x
derivative of pi/9 cos(θ)	derivative\:\frac{π}{9}\cos(θ)
integral from 0 to 1 of x^2sqrt(1-x^2)	\int\:_{0}^{1}x^{2}\sqrt{1-x^{2}}dx
f(x)=xsin(2x)	f(x)=x\sin(2x)
y^'=(4y)/x	y^{\prime\:}=\frac{4y}{x}
integral from 0 to 7 of x^2sqrt(49-x^2)	\int\:_{0}^{7}x^{2}\sqrt{49-x^{2}}dx
y^'=(2t+1)e^y	y^{\prime\:}=(2t+1)e^{y}
(\partial)/(\partial y)(ln(x^4y))	\frac{\partial\:}{\partial\:y}(\ln(x^{4}y))
derivative of (2-3x^2^4(x^7+3)^3)	\frac{d}{dx}((2-3x^{2})^{4}(x^{7}+3)^{3})
(dy)/(dx)+7y=4	\frac{dy}{dx}+7y=4
d/(dz)(sqrt(z+1)-1)	\frac{d}{dz}(\sqrt{z+1}-1)
slope of x^2+8x+2	slope\:x^{2}+8x+2
limit as x approaches 1-of (\|x-1\|)/(x-1)	\lim\:_{x\to\:1-}(\frac{\left\|x-1\right\|}{x-1})
derivative of 3-(10/(3x^{1/6)})	\frac{d}{dx}(3-\frac{10}{3x^{\frac{1}{6}}})
sum from n=1 to infinity of (1-1/n)^2	\sum\:_{n=1}^{\infty\:}(1-\frac{1}{n})^{2}
inverse oflaplace 1/(s^2-3)	inverselaplace\:\frac{1}{s^{2}-3}
integral of (2x)/((1-x^2))	\int\:\frac{2x}{(1-x^{2})}dx

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