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Popular Calculus Problems

integral of 1/(y^6)-9/(sqrt(y))	\int\:\frac{1}{y^{6}}-\frac{9}{\sqrt{y}}dy
derivative of (4a+1)^2	derivative\:(4a+1)^{2}
y^{''}+4y^'=10e^t	y^{\prime\:\prime\:}+4y^{\prime\:}=10e^{t}
derivative of (e^{4x}+e^{-4x}/x)	\frac{d}{dx}(\frac{e^{4x}+e^{-4x}}{x})
area 2x,x=3	area\:2x,x=3
f^{''}(x)=f(x)	f^{\prime\:\prime\:}(x)=f(x)
(dy)/(dx)+2y=7,y(0)=1	\frac{dy}{dx}+2y=7,y(0)=1
integral of (x^2-2)sqrt(x)	\int\:(x^{2}-2)\sqrt{x}dx
integral of (4+4x)/(1+x^2)	\int\:\frac{4+4x}{1+x^{2}}dx
f(x)=(2x+1)/(x^2+2)	f(x)=\frac{2x+1}{x^{2}+2}
slope of (-2.2)(3.4)	slope\:(-2.2)(3.4)
integral of (1+x)e^{-x}	\int\:(1+x)e^{-x}dx
derivative of (x^7/(25))	\frac{d}{dx}(\frac{x^{7}}{25})
8x^2y^'=y^'+7xe^{-y}	8x^{2}y^{\prime\:}=y^{\prime\:}+7xe^{-y}
(\partial)/(\partial x)(x/(x^4-y^5))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{4}-y^{5}})
derivative of f^8	derivative\:f^{8}
integral of sqrt(x+9)	\int\:\sqrt{x+9}dx
integral from-2 to 1 of (x-4\|x\|)	\int\:_{-2}^{1}(x-4\left\|x\right\|)dx
integral of \sqrt[3]{3-2x^2}(-4x)	\int\:\sqrt[3]{3-2x^{2}}(-4x)dx
y^{''}-4y=e^{-2x}-2x	y^{\prime\:\prime\:}-4y=e^{-2x}-2x
integral of cos(10x)cos(3x)	\int\:\cos(10x)\cos(3x)dx
tangent of f(x)=x+2/x ,\at x=3	tangent\:f(x)=x+\frac{2}{x},\at\:x=3
derivative of 1500e^x	derivative\:1500e^{x}
derivative of (x^2/(x+1))	\frac{d}{dx}(\frac{x^{2}}{x+1})
y^'+y/t =2cos(3t)	y^{\prime\:}+\frac{y}{t}=2\cos(3t)
derivative of x^2(x-1^3)	\frac{d}{dx}(x^{2}(x-1)^{3})
limit as x approaches 0 of ((2.8^x-1))/x	\lim\:_{x\to\:0}(\frac{(2.8^{x}-1)}{x})
integral from 0 to 1/2 of sqrt(1-4x^2)	\int\:_{0}^{\frac{1}{2}}\sqrt{1-4x^{2}}dx
integral of 6/(xsqrt(x^2+1))	\int\:\frac{6}{x\sqrt{x^{2}+1}}dx
integral of (x+1)e^{9x^2+18x}	\int\:(x+1)e^{9x^{2}+18x}dx
(d^2y)/(dx^2)-4(dy)/(dx)+13y=8sin(3x),y(0)=1,y^'(0)=2	\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+13y=8\sin(3x),y(0)=1,y^{\prime\:}(0)=2
limit as x approaches 1 of (9x^2)+30x+25	\lim\:_{x\to\:1}((9x^{2})+30x+25)
laplacetransform 4y	laplacetransform\:4y
integral of x^{25}sin(x^{26})	\int\:x^{25}\sin(x^{26})dx
derivative of e^5	derivative\:e^{5}
(\partial)/(\partial x)(y^2sin(x/y))	\frac{\partial\:}{\partial\:x}(y^{2}\sin(\frac{x}{y}))
derivative of i/(sqrt(5x^2+1))	\frac{d}{dx}(\frac{i}{\sqrt{5x^{2}+1}})
derivative of y=(2x^2+4x+4)/(sqrt(x))	derivative\:y=\frac{2x^{2}+4x+4}{\sqrt{x}}
integral of ln(4-x)	\int\:\ln(4-x)dx
(df^{-1})/(dx)f(x)=3x^3-5x^2-2,x=1272	\frac{df^{-1}}{dx}f(x)=3x^{3}-5x^{2}-2,x=1272
derivative of (1+x)/(1+e^x)	derivative\:\frac{1+x}{1+e^{x}}
area x=8y^2,x=20+3y^2	area\:x=8y^{2},x=20+3y^{2}
derivative of (x^2+5x+2^7)	\frac{d}{dx}((x^{2}+5x+2)^{7})
integral of x^3sqrt(64-x^2)	\int\:x^{3}\sqrt{64-x^{2}}dx
integral of xsqrt(81+x^2)	\int\:x\sqrt{81+x^{2}}dx
area y=sqrt(2x),y=12-x,y=4-x	area\:y=\sqrt{2x},y=12-x,y=4-x
tangent of f(x)=(2x-1)/(x+9),\at x=2	tangent\:f(x)=\frac{2x-1}{x+9},\at\:x=2
derivative of y=arccsc(4x)	derivative\:y=\arccsc(4x)
integral of tan^3(θ)	\int\:\tan^{3}(θ)dθ
xy^{''}+2y^'=8x^2	xy^{\prime\:\prime\:}+2y^{\prime\:}=8x^{2}
(\partial)/(\partial y)(xe^{xy^2})	\frac{\partial\:}{\partial\:y}(xe^{xy^{2}})
integral of \sqrt[3]{w}+10\sqrt[5]{w^3}	\int\:\sqrt[3]{w}+10\sqrt[5]{w^{3}}dw
limit as x approaches-1-of sqrt(-4x-4)-8	\lim\:_{x\to\:-1-}(\sqrt{-4x-4}-8)
y^'+y=(1-x)/(2x^2)	y^{\prime\:}+y=\frac{1-x}{2x^{2}}
tangent of y^6+x^3=y^2+12x,(0,1)	tangent\:y^{6}+x^{3}=y^{2}+12x,(0,1)
limit as x approaches-1 of x/0	\lim\:_{x\to\:-1}(\frac{x}{0})
tangent of f(x)=5*3^x,\at x=2	tangent\:f(x)=5\cdot\:3^{x},\at\:x=2
derivative of x^x+1	\frac{d}{dx}(x^{x}+1)
(\partial)/(\partial x)(5x^2+y+sin(axy)+3)	\frac{\partial\:}{\partial\:x}(5x^{2}+y+\sin(axy)+3)
integral of (3x(8-x))/(135)	\int\:\frac{3x(8-x)}{135}dx
derivative of y=2^xln(5)	derivative\:y=2^{x}\ln(5)
integral of x/y+y/x	\int\:\frac{x}{y}+\frac{y}{x}dy
integral from 0 to 2 of x^3sqrt(1+9x^4)	\int\:_{0}^{2}x^{3}\sqrt{1+9x^{4}}dx
derivative of 8arctan(x)	\frac{d}{dx}(8\arctan(x))
integral from 1 to e of 1/x	\int\:_{1}^{e}\frac{1}{x}dx
derivative of y=ln(1/(xsqrt(x+1)))	derivative\:y=\ln(\frac{1}{x\sqrt{x+1}})
xy^'-2y-16=0	xy^{\prime\:}-2y-16=0
y^'=e^{5y}sin(6x)	y^{\prime\:}=e^{5y}\sin(6x)
xy^'-10y=0	xy^{\prime\:}-10y=0
derivative of tan(x^6)	\frac{d}{dx}(\tan(x^{6}))
limit as x approaches 0 of (-6+x)/(x^4)	\lim\:_{x\to\:0}(\frac{-6+x}{x^{4}})
limit as x approaches-5 of (x^2-7)/(5-x)	\lim\:_{x\to\:-5}(\frac{x^{2}-7}{5-x})
integral of x(ln(x))	\int\:x(\ln(x))dx
integral of sec^5(2x)	\int\:\sec^{5}(2x)dx
limit as θ approaches 0 of (sin(5θ))/(sin(2θ))	\lim\:_{θ\to\:0}(\frac{\sin(5θ)}{\sin(2θ)})
(\partial)/(\partial x)(a/(x^2+a^2))	\frac{\partial\:}{\partial\:x}(\frac{a}{x^{2}+a^{2}})
derivative of ln(8x+9)	derivative\:\ln(8x+9)
integral of (a^{2/3}-x^{2/3})	\int\:(a^{\frac{2}{3}}-x^{\frac{2}{3}})dx
integral of 1/(sqrt(36-4x^2))	\int\:\frac{1}{\sqrt{36-4x^{2}}}dx
integral of sqrt((4-2x))	\int\:\sqrt{(4-2x)}dx
derivative of sin(x+sqrt(x))	\frac{d}{dx}(\sin(x)+\sqrt{x})
integral of (x^4-2x+1)/(x^2)	\int\:\frac{x^{4}-2x+1}{x^{2}}dx
(\partial)/(\partial x)(sin(x)yz)	\frac{\partial\:}{\partial\:x}(\sin(x)yz)
derivative of 5sin(x-0.64)	derivative\:5\sin(x-0.64)
integral of 7sqrt(16-2x)-14	\int\:7\sqrt{16-2x}-14dx
limit as x approaches-7-of (x+6)/(x+7)	\lim\:_{x\to\:-7-}(\frac{x+6}{x+7})
sum from n=1 to infinity of (x/2)^n	\sum\:_{n=1}^{\infty\:}(\frac{x}{2})^{n}
integral of (x+3)(x-7)	\int\:(x+3)(x-7)dx
area x^2-3,5-x^2	area\:x^{2}-3,5-x^{2}
(\partial)/(\partial x)(x^2+2y^2+xy^2+1)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}+xy^{2}+1)
f(t)=3sin(2t)	f(t)=3\sin(2t)
integral of x^2-5x+6	\int\:x^{2}-5x+6dx
(\partial)/(\partial x)(x^{1/4}y^{3/4})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{4}}y^{\frac{3}{4}})
derivative of cos(a^5+x^5)	derivative\:\cos(a^{5}+x^{5})
integral of x/(sqrt(x^2+16))	\int\:\frac{x}{\sqrt{x^{2}+16}}dx
(\partial)/(\partial y)(e^{5xy})	\frac{\partial\:}{\partial\:y}(e^{5xy})
integral of 9^x	\int\:9^{x}dx
tangent of f(x)=0.14x^2+0.68x+3.1	tangent\:f(x)=0.14x^{2}+0.68x+3.1
area y=sin(4x),(0, pi/4)	area\:y=\sin(4x),(0,\frac{π}{4})
y^'=2x+y,y(0)=5	y^{\prime\:}=2x+y,y(0)=5

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