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Popular Calculus Problems

(dx)/(dt)=t-x	\frac{dx}{dt}=t-x
derivative of 3cos^3(x)	\frac{d}{dx}(3\cos^{3}(x))
integral of (5x-2)^7	\int\:(5x-2)^{7}dx
(\partial)/(\partial y)(y/(1+x^2y^2))	\frac{\partial\:}{\partial\:y}(\frac{y}{1+x^{2}y^{2}})
integral from pi to 2pi of x	\int\:_{π}^{2π}xdx
integral of (-1)/(sqrt(1-(4t+1)^2))	\int\:\frac{-1}{\sqrt{1-(4t+1)^{2}}}dt
derivative of e^{x^2-1}	derivative\:e^{x^{2}-1}
limit as x approaches 0 of ln(20)	\lim\:_{x\to\:0}(\ln(20))
derivative of (6e^x/((6+e^x)^2))	\frac{d}{dx}(\frac{6e^{x}}{(6+e^{x})^{2}})
derivative of 2arctan(x)	derivative\:2\arctan(x)
limit as x approaches-3 of 7x^2	\lim\:_{x\to\:-3}(7x^{2})
integral of xe^{5x^2}	\int\:xe^{5x^{2}}dx
slope of x^2+xy+2y^2=4	slope\:x^{2}+xy+2y^{2}=4
derivative of sec(\sqrt[3]{x^5-2})	derivative\:\sec(\sqrt[3]{x^{5}-2})
integral of (x^2+1)^{3/2}	\int\:(x^{2}+1)^{\frac{3}{2}}dx
integral of-15x^4(-3x^5-1)^5	\int\:-15x^{4}(-3x^{5}-1)^{5}dx
derivative of sqrt(x)ln(4x)	\frac{d}{dx}(\sqrt{x}\ln(4x))
area 4-x,0,-2,6	area\:4-x,0,-2,6
area y=1,x=y^{5/2},[0,1]	area\:y=1,x=y^{\frac{5}{2}},[0,1]
integral of 6e^{-6x}	\int\:6e^{-6x}dx
limit as x approaches 1 of ln(x)-ln(x-1)	\lim\:_{x\to\:1}(\ln(x)-\ln(x-1))
limit as x approaches 0 of x/(x^2+y^2)	\lim\:_{x\to\:0}(\frac{x}{x^{2}+y^{2}})
integral of 1/(x^2+8)	\int\:\frac{1}{x^{2}+8}dx
integral of 1/(xsqrt(9x^2+1))	\int\:\frac{1}{x\sqrt{9x^{2}+1}}dx
integral of (x^8)	\int\:(x^{8})dx
tangent of f(x)=x^3-9x,(3,0)	tangent\:f(x)=x^{3}-9x,(3,0)
tangent of f(x)=(4x)/(x+2),(6,3)	tangent\:f(x)=\frac{4x}{x+2},(6,3)
derivative of f(x)=sqrt(x^2+5x)	derivative\:f(x)=\sqrt{x^{2}+5x}
derivative of e^{sqrt(ln(x^2+1+x)})	\frac{d}{dx}(e^{\sqrt{\ln(x^{2}+1)+x}})
integral from-1 to 6 of (9y)/(y^2-5y-14)	\int\:_{-1}^{6}\frac{9y}{y^{2}-5y-14}dy
integral from 1 to 2 of (4/x-(16)/(x^2))	\int\:_{1}^{2}(\frac{4}{x}-\frac{16}{x^{2}})dx
y^'-2ty=t	y^{\prime\:}-2ty=t
integral of (5cos^2(x))/(sin(x))	\int\:\frac{5\cos^{2}(x)}{\sin(x)}dx
tangent of y=(8x)/((x^2+1)),\at	tangent\:y=\frac{8x}{(x^{2}+1)},\at
integral of sec(6x)tan(6x)	\int\:\sec(6x)\tan(6x)dx
(\partial)/(\partial x)(1/(sqrt(1+x^2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{1+x^{2}}})
derivative of 1/16 e^{2x^2}	\frac{d}{dx}(\frac{1}{16}e^{2x^{2}})
area y=2x+2,y=x^2+2,x=-1,x=3	area\:y=2x+2,y=x^{2}+2,x=-1,x=3
limit as x approaches-pi of (sin(x))/x	\lim\:_{x\to\:-π}(\frac{\sin(x)}{x})
integral of 2t+1	\int\:2t+1dt
derivative of y=ln(sqrt(1-x^2))	derivative\:y=\ln(\sqrt{1-x^{2}})
integral from 0 to y of 0.5	\int\:_{0}^{y}0.5dx
derivative of f(x)=cos(sqrt(sin(tan(pix))))	derivative\:f(x)=\cos(\sqrt{\sin(\tan(πx))})
limit as x approaches 4 of ln\|x-4\|	\lim\:_{x\to\:4}(\ln\left\|x-4\right\|)
x^3+3y-xy^'=0	x^{3}+3y-xy^{\prime\:}=0
limit as x approaches pi/2 of tan^2(x)	\lim\:_{x\to\:\frac{π}{2}}(\tan^{2}(x))
y^{''}+2y^'+y=sin(x)+6cos(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=\sin(x)+6\cos(2x)
limit as x approaches-2 of x^3+6x^2-16	\lim\:_{x\to\:-2}(x^{3}+6x^{2}-16)
integral of ((cos^2(x)))/(sin(x))	\int\:\frac{(\cos^{2}(x))}{\sin(x)}dx
integral of 1/((2x+3)^2)	\int\:\frac{1}{(2x+3)^{2}}dx
laplacetransform cos^2(4t)	laplacetransform\:\cos^{2}(4t)
y^{''}-y^'-6y=e^{2x}	y^{\prime\:\prime\:}-y^{\prime\:}-6y=e^{2x}
derivative of f(x)=8x^7	derivative\:f(x)=8x^{7}
implicit (dy)/(dx),7x+4y=2	implicit\:\frac{dy}{dx},7x+4y=2
integral of (x+2)/((x+1)^2)	\int\:\frac{x+2}{(x+1)^{2}}dx
integral from 0 to 10 of 9800pi(10-y)	\int\:_{0}^{10}9800π(10-y)dy
derivative of (x^2+1(x+5+1/x))	\frac{d}{dx}((x^{2}+1)(x+5+\frac{1}{x}))
limit as x approaches 0 of (ln(e^x-x))/x	\lim\:_{x\to\:0}(\frac{\ln(e^{x}-x)}{x})
(\partial)/(\partial x)((8x)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{8x}{x^{2}+y^{2}})
(\partial)/(\partial b)((a^3b^4)/(c^2d^4))	\frac{\partial\:}{\partial\:b}(\frac{a^{3}b^{4}}{c^{2}d^{4}})
(\partial)/(\partial x)(-e^{-x-y})	\frac{\partial\:}{\partial\:x}(-e^{-x-y})
integral from 1/2 to 1 of (x^{-3}-24)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-24)dx
y^{''}+2y^'+y=2	y^{\prime\:\prime\:}+2y^{\prime\:}+y=2
limit as x approaches 0 of x*e^x	\lim\:_{x\to\:0}(x\cdot\:e^{x})
derivative of (10log_{4}(x)/x)	\frac{d}{dx}(\frac{10\log_{4}(x)}{x})
limit as x approaches infinity of (6^{x+1})/(7^{x-1)}	\lim\:_{x\to\:\infty\:}(\frac{6^{x+1}}{7^{x-1}})
integral of (x-3)sin(pix)	\int\:(x-3)\sin(πx)dx
integral of (cot(sqrt(x)))/(sqrt(x))	\int\:\frac{\cot(\sqrt{x})}{\sqrt{x}}dx
(\partial)/(\partial x)(ln(x+4y+7z))	\frac{\partial\:}{\partial\:x}(\ln(x+4y+7z))
derivative of (x-1^2+1)	\frac{d}{dx}((x-1)^{2}+1)
(\partial)/(\partial x)(cos(ye^{x*y}))	\frac{\partial\:}{\partial\:x}(\cos(ye^{x\cdot\:y}))
integral of [1+1/((x+1)^2)]	\int\:[1+\frac{1}{(x+1)^{2}}]dx
limit as x approaches 2 of 4-x	\lim\:_{x\to\:2}(4-x)
derivative of y=(x^5)/(3-x^4)	derivative\:y=\frac{x^{5}}{3-x^{4}}
(\partial)/(\partial y)(ln(2x^2+y^2))	\frac{\partial\:}{\partial\:y}(\ln(2x^{2}+y^{2}))
limit as x approaches 4 of (x-4)/(x^2+3x-28)	\lim\:_{x\to\:4}(\frac{x-4}{x^{2}+3x-28})
limit as x approaches infinity of x/(12)	\lim\:_{x\to\:\infty\:}(\frac{x}{12})
derivative of (sqrt(x)-7/(sqrt(x)+5))	\frac{d}{dx}(\frac{\sqrt{x}-7}{\sqrt{x}+5})
(\partial)/(\partial x)(x^2yz-xyz^5)	\frac{\partial\:}{\partial\:x}(x^{2}yz-xyz^{5})
y^{'''}-y^{''}+7y^'-7y=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+7y^{\prime\:}-7y=0
limit as x approaches 0 of x^3x	\lim\:_{x\to\:0}(x^{3}x)
integral from 0 to 5 of (x+y)/(55)	\int\:_{0}^{5}\frac{x+y}{55}dx
(\partial)/(\partial x)(4arctan(y/x))	\frac{\partial\:}{\partial\:x}(4\arctan(\frac{y}{x}))
derivative of sin(e^x(x^2-x))	\frac{d}{dx}(\sin(e^{x}(x^{2}-x)))
tangent of 2x^2-2x-4,\at x=1	tangent\:2x^{2}-2x-4,\at\:x=1
derivative of (cos(x))/(x^5)	derivative\:\frac{\cos(x)}{x^{5}}
derivative of x/(6-x)	\frac{d}{dx}(\frac{x}{6-x})
limit as x approaches 2 of 8-3x+12x^2	\lim\:_{x\to\:2}(8-3x+12x^{2})
derivative of (56/(x^9))	\frac{d}{dx}(\frac{56}{x^{9}})
integral from 0 to 3 of 1/x	\int\:_{0}^{3}\frac{1}{x}dx
derivative of (27/((x+5)^{4/3)})	\frac{d}{dx}(\frac{27}{(x+5)^{\frac{4}{3}}})
integral of sin(t)*sin(t)	\int\:\sin(t)\cdot\:\sin(t)dt
limit as n approaches infinity of 7n^{5/4}	\lim\:_{n\to\:\infty\:}(7n^{\frac{5}{4}})
y^'-y=9te^2t,y(0)=1	y^{\prime\:}-y=9te^{2}t,y(0)=1
integral of-(1-cos^2(x))/(cos(x))	\int\:-\frac{1-\cos^{2}(x)}{\cos(x)}dx
integral from 0 to pi/4 of cos^4(x)	\int\:_{0}^{\frac{π}{4}}\cos^{4}(x)dx
derivative of 25x^4+30x^3-11x^2-12x+4	derivative\:25x^{4}+30x^{3}-11x^{2}-12x+4
(5t+3y+6)dt-dy=0	(5t+3y+6)dt-dy=0
y^'-3y=9x	y^{\prime\:}-3y=9x
slope of (-3,-1),(8,2)	slope\:(-3,-1),(8,2)

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