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Popular Calculus Problems

y^'+3y=e^{-2x}	y^{\prime\:}+3y=e^{-2x}
integral from-3 to 4 of ((y+12)-(y^2))	\int\:_{-3}^{4}((y+12)-(y^{2}))dy
y^{''}+7y^'+6y=0	y^{\prime\:\prime\:}+7y^{\prime\:}+6y=0
derivative of f(x)=2(x)^3ln(x)	derivative\:f(x)=2(x)^{3}\ln(x)
limit as x approaches-2 of (x^2+4)/(x+2)	\lim\:_{x\to\:-2}(\frac{x^{2}+4}{x+2})
area y=-x^2+10,y=-1.5x+7	area\:y=-x^{2}+10,y=-1.5x+7
derivative of sqrt((x^2-x^4/8))	\frac{d}{dx}(\sqrt{\frac{x^{2}-x^{4}}{8}})
derivative of x-arcsin(x)	\frac{d}{dx}(x-\arcsin(x))
y^'=(sin(x))/(cos(y))	y^{\prime\:}=\frac{\sin(x)}{\cos(y)}
f(x)=4log_{2}(x)	f(x)=4\log_{2}(x)
integral of 7/(x^2sqrt(1+x^2))	\int\:\frac{7}{x^{2}\sqrt{1+x^{2}}}dx
derivative of x^2e^{-x^2}	derivative\:x^{2}e^{-x^{2}}
integral of 1/2 cos(4x)	\int\:\frac{1}{2}\cos(4x)dx
derivative of f(x)=(x^3+7x+2)9+1/(x^2)	derivative\:f(x)=(x^{3}+7x+2)9+\frac{1}{x^{2}}
integral of ((arctan(x)))/x	\int\:\frac{(\arctan(x))}{x}dx
2x((dy)/(dx))+y=10sqrt(x)	2x(\frac{dy}{dx})+y=10\sqrt{x}
integral of 1/(e^x+2e^{-x)+2}	\int\:\frac{1}{e^{x}+2e^{-x}+2}dx
integral of (csc(5/(x^3)))/(x^4)	\int\:\frac{\csc(\frac{5}{x^{3}})}{x^{4}}dx
tangent of f(x)=x^2+x,(2,-3)	tangent\:f(x)=x^{2}+x,(2,-3)
limit as x approaches 8+of 1/((x-8))	\lim\:_{x\to\:8+}(\frac{1}{(x-8)})
(7x+3y)dx+(3x-8y3)dy=0	(7x+3y)dx+(3x-8y3)dy=0
derivative of (kx+a)/(bx+c)	derivative\:\frac{kx+a}{bx+c}
(\partial)/(\partial z)(zsin(y))	\frac{\partial\:}{\partial\:z}(z\sin(y))
integral from 0 to 3 of (5t)/((t-4)^2)	\int\:_{0}^{3}\frac{5t}{(t-4)^{2}}dt
(dy)/(dx)=(cos(15x))/(e^{15y)}	\frac{dy}{dx}=\frac{\cos(15x)}{e^{15y}}
9t((dy)/(dt))+y=t^2	9t(\frac{dy}{dt})+y=t^{2}
(\partial)/(\partial y)((e^{2y})/(2x))	\frac{\partial\:}{\partial\:y}(\frac{e^{2y}}{2x})
integral from 1 to e of 4x^2ln(x)	\int\:_{1}^{e}4x^{2}\ln(x)dx
derivative of 1/(sqrt(1+x))	\frac{d}{dx}(\frac{1}{\sqrt{1+x}})
derivative of e^{1/2}	\frac{d}{dx}(e^{\frac{1}{2}})
integral of (1-x)/(x^3)	\int\:\frac{1-x}{x^{3}}dx
(dy)/(dx)=(x-18)^2	\frac{dy}{dx}=(x-18)^{2}
limit as x approaches 4 of 9/x	\lim\:_{x\to\:4}(\frac{9}{x})
inverse oflaplace (2s)/((s^2+25)(s-1))	inverselaplace\:\frac{2s}{(s^{2}+25)(s-1)}
derivative of y=(2x)/(x^2-1)	derivative\:y=\frac{2x}{x^{2}-1}
area y=2-x^2,y=x	area\:y=2-x^{2},y=x
limit as x approaches-2 of (-5x-10)/(x^3+2x^2)	\lim\:_{x\to\:-2}(\frac{-5x-10}{x^{3}+2x^{2}})
derivative of (6x)/(sqrt(x^2+2))	derivative\:\frac{6x}{\sqrt{x^{2}+2}}
(dy)/(dx)= 1/(xsqrt(16x^2-1))	\frac{dy}{dx}=\frac{1}{x\sqrt{16x^{2}-1}}
derivative of f(x)=(x^2-4)(x+1)	derivative\:f(x)=(x^{2}-4)(x+1)
area 4x,x^2-12	area\:4x,x^{2}-12
t^2y^{''}+7ty^'+5y=0	t^{2}y^{\prime\:\prime\:}+7ty^{\prime\:}+5y=0
derivative of x^2-sqrt(x)+5	\frac{d}{dx}(x^{2}-\sqrt{x}+5)
integral from 1 to 4 of 1/(x^2)	\int\:_{1}^{4}\frac{1}{x^{2}}dx
derivative of 1/((1+x^2))	derivative\:\frac{1}{(1+x^{2})}
derivative of (x+2^{2x-3})	\frac{d}{dx}((x+2)^{2x-3})
d/(dt)(e^{-it})	\frac{d}{dt}(e^{-it})
limit as x approaches 6 of cx^2+9x	\lim\:_{x\to\:6}(cx^{2}+9x)
(\partial}{\partial u}(\frac{v-u)/2)	\frac{\partial\:}{\partial\:u}(\frac{v-u}{2})
slope of (-3,-8),(5,6)	slope\:(-3,-8),(5,6)
(\partial)/(\partial x)(x^2y+2y^2-6x+3y-4)	\frac{\partial\:}{\partial\:x}(x^{2}y+2y^{2}-6x+3y-4)
integral of 2/(sqrt(1-x^2))	\int\:\frac{2}{\sqrt{1-x^{2}}}dx
d/(d{y)}(e^{{y}{z}})	\frac{d}{d{y}}(e^{{y}{z}})
integral from 1 to 2 of 6/(x^2)	\int\:_{1}^{2}\frac{6}{x^{2}}dx
integral from-3 to 3 of (2-\|x\|)	\int\:_{-3}^{3}(2-\left\|x\right\|)dx
derivative of sqrt(x^6)	\frac{d}{dx}(\sqrt{x^{6}})
derivative of (2x-sqrt(x)(5x+2))	\frac{d}{dx}((2x-\sqrt{x})(5x+2))
integral of (sin^2(x))/(cos^4(x))	\int\:\frac{\sin^{2}(x)}{\cos^{4}(x)}dx
sum from n=0 to infinity of e^{-0.06n}	\sum\:_{n=0}^{\infty\:}e^{-0.06n}
y^{''}-5y^'+6y=2e^{t/2}	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=2e^{\frac{t}{2}}
derivative of csc^7(2x^pi+pi^3)	\frac{d}{dx}(\csc^{7}(2x^{π}+π^{3}))
area sin^2(x),sin^4(x),[0,pi]	area\:\sin^{2}(x),\sin^{4}(x),[0,π]
integral of (4x+1)sqrt(x-5)	\int\:(4x+1)\sqrt{x-5}dx
(dy)/(dx)=3cos(7x)	\frac{dy}{dx}=3\cos(7x)
derivative of g(x)=sqrt(x)+5	derivative\:g(x)=\sqrt{x}+5
integral of 4x-2sqrt(x)	\int\:4x-2\sqrt{x}dx
integral of e^2ln(x)	\int\:e^{2}\ln(x)dx
integral of x/(sqrt(1-9x^2))	\int\:\frac{x}{\sqrt{1-9x^{2}}}dx
limit as x approaches 4 of (\|4-x\|)/(4-x)	\lim\:_{x\to\:4}(\frac{\left\|4-x\right\|}{4-x})
integral of (2x^{-1})	\int\:(2x^{-1})dx
2y^{''}+y^'-3y=0	2y^{\prime\:\prime\:}+y^{\prime\:}-3y=0
y^'= y/(4x)	y^{\prime\:}=\frac{y}{4x}
(\partial)/(\partial x)(2x^2+3y^2-20)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}-20)
derivative of sqrt(y/3)	derivative\:\sqrt{\frac{y}{3}}
integral of (e^{2x})/(-2)	\int\:\frac{e^{2x}}{-2}dx
integral from 0 to infinity of 1/(9+x^2)	\int\:_{0}^{\infty\:}\frac{1}{9+x^{2}}dx
integral of 1/((x^2+2x))	\int\:\frac{1}{(x^{2}+2x)}dx
derivative of x^2-x^3+4	derivative\:x^{2}-x^{3}+4
limit as x approaches infinity of x^3-1	\lim\:_{x\to\:\infty\:}(x^{3}-1)
(\partial)/(\partial x)(sqrt(x^2+y^2)-x)	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}}-x)
y^'=-((2x+ln(y))y)/x	y^{\prime\:}=-\frac{(2x+\ln(y))y}{x}
derivative of y=x^2sin(pix)	derivative\:y=x^{2}\sin(πx)
(\partial)/(\partial x)(-5x^2-2xy-3y^2)	\frac{\partial\:}{\partial\:x}(-5x^{2}-2xy-3y^{2})
derivative of arccot(x/9)	derivative\:\arccot(\frac{x}{9})
integral of (sqrt(x)-1)/(sqrt(x)+1)	\int\:\frac{\sqrt{x}-1}{\sqrt{x}+1}dx
integral of (2x+3)/((x+1)^2)	\int\:\frac{2x+3}{(x+1)^{2}}dx
implicit 8x^2+7y^2=56	implicit\:8x^{2}+7y^{2}=56
derivative of (x^2/(2(1-x)))	\frac{d}{dx}(\frac{x^{2}}{2(1-x)})
(\partial)/(\partial y)((x^3+2y^2)^3)	\frac{\partial\:}{\partial\:y}((x^{3}+2y^{2})^{3})
f(x)=(cot(x))/(1+cot(x))	f(x)=\frac{\cot(x)}{1+\cot(x)}
(1+e^t)y^'+e^ty=0	(1+e^{t})y^{\prime\:}+e^{t}y=0
integral of (e^{1/t})/(t^3)	\int\:\frac{e^{\frac{1}{t}}}{t^{3}}dt
derivative of e^y	derivative\:e^{y}
integral of cos(x)(2+sin(x))^5	\int\:\cos(x)(2+\sin(x))^{5}dx
limit as x approaches 0 of x^2+2x-2	\lim\:_{x\to\:0}(x^{2}+2x-2)
(\partial)/(\partial x)(e^xln(1+y))	\frac{\partial\:}{\partial\:x}(e^{x}\ln(1+y))
(x+1)(dy)/(dx)+y=ln(x),y(1)=10	(x+1)\frac{dy}{dx}+y=\ln(x),y(1)=10
(\partial)/(\partial x)(7ye^{5x})	\frac{\partial\:}{\partial\:x}(7ye^{5x})
area y=ln(x),y=0,x=4e	area\:y=\ln(x),y=0,x=4e
integral of ((1-3x))/(sqrt(2x-3x^2))	\int\:\frac{(1-3x)}{\sqrt{2x-3x^{2}}}dx

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