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Popular Calculus Problems

(dy)/(dx)+9y=3	\frac{dy}{dx}+9y=3
integral of (14)/(1-cos(7x))	\int\:\frac{14}{1-\cos(7x)}dx
y^{''}+2y=cos(t)-2*sin(2t)	y^{\prime\:\prime\:}+2y=\cos(t)-2\cdot\:\sin(2t)
integral of 3e^{-3x}	\int\:3e^{-3x}dx
y^{''}-2y^'+y=t^{-3}e^t	y^{\prime\:\prime\:}-2y^{\prime\:}+y=t^{-3}e^{t}
(dy}{dx}+(3y)/x =\frac{e^x)/(x^3)	\frac{dy}{dx}+\frac{3y}{x}=\frac{e^{x}}{x^{3}}
integral of-2x+4	\int\:-2x+4dx
(\partial)/(\partial x)(-8x)	\frac{\partial\:}{\partial\:x}(-8x)
integral of (x+2)^2	\int\:(x+2)^{2}dx
integral of 6x^3e^{x^4}	\int\:6x^{3}e^{x^{4}}dx
integral of 4x^2cos(mx)	\int\:4x^{2}\cos(mx)dx
integral of sqrt(x-3)	\int\:\sqrt{x-3}dx
integral of (7-1/(x^6))^2(1/(x^7))	\int\:(7-\frac{1}{x^{6}})^{2}(\frac{1}{x^{7}})dx
f(t)=e^t-1	f(t)=e^{t}-1
derivative of 3sqrt(x)-x	\frac{d}{dx}(3\sqrt{x}-x)
f(x)=(ln(x))/(x^4)	f(x)=\frac{\ln(x)}{x^{4}}
area y=2sin(x)+sin(2x),x=0,x=pi	area\:y=2\sin(x)+\sin(2x),x=0,x=π
(dy)/(dt)=y+1+2*sin(t)	\frac{dy}{dt}=y+1+2\cdot\:\sin(t)
derivative of ln(p)	derivative\:\ln(p)
derivative of f(t)=3t+4(t)^2	derivative\:f(t)=3t+4(t)^{2}
integral of (3+5x-6x^2-7x^3)/(2x^2)	\int\:\frac{3+5x-6x^{2}-7x^{3}}{2x^{2}}dx
derivative of xcos(xsin(x))	\frac{d}{dx}(x\cos(x)\sin(x))
integral of t/(t^4+7)	\int\:\frac{t}{t^{4}+7}dt
derivative of-xcos(x)	derivative\:-x\cos(x)
dy=(x+2y)dx	dy=(x+2y)dx
integral of (x^2-1)/((x-2)^2(x+3))	\int\:\frac{x^{2}-1}{(x-2)^{2}(x+3)}dx
(\partial)/(\partial x)(x/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{(x+y)^{2}})
integral of xe^{x^5}	\int\:xe^{x^{5}}dx
slope of (8-1)(82)	slope\:(8-1)(82)
taylor \sqrt[3]{x+8}	taylor\:\sqrt[3]{x+8}
derivative of 36x	\frac{d}{dx}(36x)
3y^'-8y=e^{-pit^2},y(0)=a	3y^{\prime\:}-8y=e^{-πt^{2}},y(0)=a
derivative of ({g}(x)/(1+{f)(x)})	\frac{d}{dx}(\frac{{g}(x)}{1+{f}(x)})
derivative of 8sin(3x)	\frac{d}{dx}(8\sin(3x))
limit as x approaches (+pi)/2 of 4sec(x)	\lim\:_{x\to\:\frac{+π}{2}}(4\sec(x))
integral of 1/((4x^2+9)^2)	\int\:\frac{1}{(4x^{2}+9)^{2}}dx
integral of (x^2)/((x^2+2x+2)^2)	\int\:\frac{x^{2}}{(x^{2}+2x+2)^{2}}dx
derivative of sin(x^3)	derivative\:\sin(x^{3})
limit as x approaches 0 of-3x^3-7x+8	\lim\:_{x\to\:0}(-3x^{3}-7x+8)
integral from-2 to 2 of 5	\int\:_{-2}^{2}5dx
y^{''}+9y^'+20y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+9y^{\prime\:}+20y=0,y(0)=1,y^{\prime\:}(0)=0
(dy)/(dx)=(3x)/(e^y)	\frac{dy}{dx}=\frac{3x}{e^{y}}
(dy)/(dx)=(-y^2)/(1+y^2)e^{(-x)},y(0)=1	\frac{dy}{dx}=\frac{-y^{2}}{1+y^{2}}e^{(-x)},y(0)=1
integral of (x^2-5x+16)/(x(x-2)^2)	\int\:\frac{x^{2}-5x+16}{x(x-2)^{2}}dx
area y=12x,y=x^2	area\:y=12x,y=x^{2}
sum from n=0 to infinity of (2)^n	\sum\:_{n=0}^{\infty\:}(2)^{n}
derivative of (x^3/3)	\frac{d}{dx}(\frac{x^{3}}{3})
y^{''}-2y^'=8x+e^x	y^{\prime\:\prime\:}-2y^{\prime\:}=8x+e^{x}
integral of (x+1)^{1/3}	\int\:(x+1)^{\frac{1}{3}}dx
integral of (8x^3+2x+2)/(2x+1)	\int\:\frac{8x^{3}+2x+2}{2x+1}dx
derivative of ln((x^2sin(x)/(2x+1)))	\frac{d}{dx}(\ln(\frac{x^{2}\sin(x)}{2x+1}))
area 2x^3+x^2-x-1,x^3+2x^2+5x-1	area\:2x^{3}+x^{2}-x-1,x^{3}+2x^{2}+5x-1
derivative of (2x-2)^4(x^2+x+1)^5	derivative\:(2x-2)^{4}(x^{2}+x+1)^{5}
longdivision (x+1)/(x-2)	longdivision\:\frac{x+1}{x-2}
derivative of e^{1/(x^2})	\frac{d}{dx}(e^{\frac{1}{x^{2}}})
limit as x approaches-2 of \sqrt[3]{x+2}cos(5/((x+2)^2))	\lim\:_{x\to\:-2}(\sqrt[3]{x+2}\cos(\frac{5}{(x+2)^{2}}))
integral from-1 to 1 of 1/(x^2+1)	\int\:_{-1}^{1}\frac{1}{x^{2}+1}dx
y^{''}+4y=-4sec(2t)	y^{\prime\:\prime\:}+4y=-4\sec(2t)
x^{''}+4x^'+5x=0	x^{\prime\:\prime\:}+4x^{\prime\:}+5x=0
(\partial)/(\partial n)(nm)	\frac{\partial\:}{\partial\:n}(nm)
limit as x approaches 2 of (3x+2)/(x+2)	\lim\:_{x\to\:2}(\frac{3x+2}{x+2})
integral from 0 to 2 of (2x+2-x^2-2)	\int\:_{0}^{2}(2x+2-x^{2}-2)dx
limit as x approaches infinity of (ln(x^2-x+1))/(ln(x^{10)+x+1)}	\lim\:_{x\to\:\infty\:}(\frac{\ln(x^{2}-x+1)}{\ln(x^{10}+x+1)})
(\partial)/(\partial x)(3sin(2x))	\frac{\partial\:}{\partial\:x}(3\sin(2x))
integral of 1/(sqrt(3-x))	\int\:\frac{1}{\sqrt{3-x}}dx
(\partial)/(\partial y)(2y^3-3y^2-12y+6)	\frac{\partial\:}{\partial\:y}(2y^{3}-3y^{2}-12y+6)
(x^2+1)y^'+8x(y-1)=0,y(0)=4	(x^{2}+1)y^{\prime\:}+8x(y-1)=0,y(0)=4
integral of xe^{(-x)/2}	\int\:xe^{\frac{-x}{2}}dx
integral from 0 to 1 of 8ln(x)	\int\:_{0}^{1}8\ln(x)dx
integral of (1+e^x)	\int\:(1+e^{x})dx
sum from n=1 to infinity of 8/((n+1)!)	\sum\:_{n=1}^{\infty\:}\frac{8}{(n+1)!}
integral of (10-x)	\int\:(10-x)dx
maclaurin sqrt(1-x/3)	maclaurin\:\sqrt{1-\frac{x}{3}}
derivative of (\|x-2\|)/(x^2)	derivative\:\frac{\left\|x-2\right\|}{x^{2}}
derivative of (100/((1+5x)^3))	\frac{d}{dx}(\frac{100}{(1+5x)^{3}})
integral of (1+tan(x))/(1-tan(x))	\int\:\frac{1+\tan(x)}{1-\tan(x)}dx
limit as x approaches infinity of (1-1/(4x))^{8x}	\lim\:_{x\to\:\infty\:}((1-\frac{1}{4x})^{8x})
integral of 1/(x^2e^{1/x)}	\int\:\frac{1}{x^{2}e^{\frac{1}{x}}}dx
integral of (5x-1)(3x^2+2)	\int\:(5x-1)(3x^{2}+2)dx
integral of e^{x^3}(12x^2)	\int\:e^{x^{3}}(12x^{2})dx
(\partial)/(\partial x)(xe^{-y/x})	\frac{\partial\:}{\partial\:x}(xe^{-\frac{y}{x}})
laplacetransform f(t)= 3/5 e^{-t}-22/5 e^{4t}	laplacetransform\:f(t)=\frac{3}{5}e^{-t}-\frac{22}{5}e^{4t}
integral of (3/(x^2)-1)	\int\:(\frac{3}{x^{2}}-1)dx
(dy)/(dx)=2-y	\frac{dy}{dx}=2-y
y^{''}-8y^'+16y=0,y(0)=2,y^'(0)=2	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=0,y(0)=2,y^{\prime\:}(0)=2
integral of 1/(sqrt(9x^2+5))	\int\:\frac{1}{\sqrt{9x^{2}+5}}dx
144y^{'''}+120y^{''}+25y^'=0	144y^{\prime\:\prime\:\prime\:}+120y^{\prime\:\prime\:}+25y^{\prime\:}=0
integral of (4x+7)e^x	\int\:(4x+7)e^{x}dx
integral of 30x^{29}	\int\:30x^{29}dx
(d^2)/(dx^2)((3x+2)/(2x-5))	\frac{d^{2}}{dx^{2}}(\frac{3x+2}{2x-5})
25y^{''}-20y^'+4y=0,y(5)=0,y^'(0)=-e^2	25y^{\prime\:\prime\:}-20y^{\prime\:}+4y=0,y(5)=0,y^{\prime\:}(0)=-e^{2}
area x=y^2+1,x=y+3	area\:x=y^{2}+1,x=y+3
(\partial)/(\partial x)(6x-6y+5xy)	\frac{\partial\:}{\partial\:x}(6x-6y+5xy)
derivative of tan(sin(sqrt(5x)))	\frac{d}{dx}(\tan(\sin(\sqrt{5x})))
integral of 6x^6-x	\int\:6x^{6}-xdx
(\partial)/(\partial x)(sqrt(y^2+cos^2(x)))	\frac{\partial\:}{\partial\:x}(\sqrt{y^{2}+\cos^{2}(x)})
integral of xsqrt(64+x^2)	\int\:x\sqrt{64+x^{2}}dx
integral of x(3sec^2(x)+tan^2(x))	\int\:x(3\sec^{2}(x)+\tan^{2}(x))dx
derivative of sqrt(cos(5x))	\frac{d}{dx}(\sqrt{\cos(5x)})
integral from 0 to pi/2 of 5cos^5(x)	\int\:_{0}^{\frac{π}{2}}5\cos^{5}(x)dx

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