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Popular Calculus Problems

area y=6x^2,y^2= 1/6 x	area\:y=6x^{2},y^{2}=\frac{1}{6}x
y^{''}+4y=-4sin(2t)	y^{\prime\:\prime\:}+4y=-4\sin(2t)
integral of (2x)/(x^2+4)	\int\:\frac{2x}{x^{2}+4}dx
derivative of sin((pix^3))	\frac{d}{dx}(\sin((πx)^{3}))
derivative of (2x+1)^4	derivative\:(2x+1)^{4}
limit as x approaches infinity of log_{2}(((x+2))/((2*x+1)))	\lim\:_{x\to\:\infty\:}(\log_{2}(\frac{(x+2)}{(2\cdot\:x+1)}))
integral from 1 to 8 of sqrt(x-1)	\int\:_{1}^{8}\sqrt{x-1}dx
tangent of x^2sqrt(x^3+1)	tangent\:x^{2}\sqrt{x^{3}+1}
integral of (sec^2(θ))/(tan(θ))	\int\:\frac{\sec^{2}(θ)}{\tan(θ)}dθ
x^{''}-2x^'-3x=0	x^{\prime\:\prime\:}-2x^{\prime\:}-3x=0
derivative of 2sqrt(xy)	\frac{d}{dx}(2\sqrt{xy})
x^'=6(x^2+1)	x^{\prime\:}=6(x^{2}+1)
derivative of 10^{x^2}	\frac{d}{dx}(10^{x^{2}})
integral from 0 to 4 of 1/(sqrt(9+x^2))	\int\:_{0}^{4}\frac{1}{\sqrt{9+x^{2}}}dx
(\partial)/(\partial x)(-6x+12)	\frac{\partial\:}{\partial\:x}(-6x+12)
area y^2=4x,y=4x-2	area\:y^{2}=4x,y=4x-2
derivative of y= 1/(sqrt(x)),x=a	derivative\:y=\frac{1}{\sqrt{x}},x=a
derivative of a/(y^{10)}	derivative\:\frac{a}{y^{10}}
f(x)=4x^{1/2}	f(x)=4x^{\frac{1}{2}}
integral from 0 to 12 of xe^{-x}	\int\:_{0}^{12}xe^{-x}dx
derivative of y=e^{3x}cos(2x)	derivative\:y=e^{3x}\cos(2x)
derivative of 7/(x^2+3)	derivative\:\frac{7}{x^{2}+3}
integral from-1 to 1 of e^y-y^2-6	\int\:_{-1}^{1}e^{y}-y^{2}-6dy
integral of sin^5(t)	\int\:\sin^{5}(t)dt
integral of (x^{20}-5x^4)^6(x^{19}-x^3)	\int\:(x^{20}-5x^{4})^{6}(x^{19}-x^{3})dx
integral of ((x^2+1))/((x+1)^2)e^x	\int\:\frac{(x^{2}+1)}{(x+1)^{2}}e^{x}dx
tangent of f(x)=x^2+5x-3,\at x=-3	tangent\:f(x)=x^{2}+5x-3,\at\:x=-3
(\partial)/(\partial y)(e^{1+x^2-y^2})	\frac{\partial\:}{\partial\:y}(e^{1+x^{2}-y^{2}})
derivative of 3/(x^4+2)	\frac{d}{dx}(\frac{3}{x^{4}+2})
tangent of f(x)=x^2-1/x ,(2,3.5)	tangent\:f(x)=x^{2}-\frac{1}{x},(2,3.5)
sum from n=1 to infinity}(((-7)^{n-1 of))/(8^n)	\sum\:_{n=1}^{\infty\:}\frac{((-7)^{n-1})}{8^{n}}
y^{''}-14y^'+49y=t^{-2}e^{7t}	y^{\prime\:\prime\:}-14y^{\prime\:}+49y=t^{-2}e^{7t}
limit as x approaches-infinity of 7/x-4	\lim\:_{x\to\:-\infty\:}(\frac{7}{x}-4)
integral of 1/(w^3)	\int\:\frac{1}{w^{3}}dw
derivative of 12sqrt(x)+16x^{3/4}	derivative\:12\sqrt{x}+16x^{\frac{3}{4}}
area f(x)=x^2-4,(-2,3)	area\:f(x)=x^{2}-4,(-2,3)
limit as x approaches 1 of x(x-1)^{-1}	\lim\:_{x\to\:1}(x(x-1)^{-1})
derivative of in	\frac{d}{dx}(in)
y^{''}+ay^'=0	y^{\prime\:\prime\:}+ay^{\prime\:}=0
integral of 12cos(3x)	\int\:12\cos(3x)dx
integral of 1+sec(x)	\int\:1+\sec(x)dx
integral of (x-y^3+y^2sin(x))	\int\:(x-y^{3}+y^{2}\sin(x))dx
integral of 1/(sqrt(-x^2+2x+15))	\int\:\frac{1}{\sqrt{-x^{2}+2x+15}}dx
inverse oflaplace 6/s+(32)/(s^2+16)	inverselaplace\:\frac{6}{s}+\frac{32}{s^{2}+16}
inverse oflaplace 8/((s^2+1)^2)	inverselaplace\:\frac{8}{(s^{2}+1)^{2}}
x^2(dy)/(dx)-y^2=0	x^{2}\frac{dy}{dx}-y^{2}=0
limit as x approaches 0 of x(ln(x))^2	\lim\:_{x\to\:0}(x(\ln(x))^{2})
integral of 4/(2x+1)	\int\:\frac{4}{2x+1}dx
tangent of 3x^4+2e^x,\at x=0	tangent\:3x^{4}+2e^{x},\at\:x=0
(x^2e^{-x})^'	(x^{2}e^{-x})^{\prime\:}
integral of \sqrt[3]{z}	\int\:\sqrt[3]{z}dz
limit as x approaches infinity of 8x^2+3	\lim\:_{x\to\:\infty\:}(8x^{2}+3)
integral from-2 to 3 of (2-\|x-1\|)	\int\:_{-2}^{3}(2-\left\|x-1\right\|)dx
limit as x approaches 0 of ((5^x-3^x))/x	\lim\:_{x\to\:0}(\frac{(5^{x}-3^{x})}{x})
derivative of (50x/(0.01x^2+1))	\frac{d}{dx}(\frac{50x}{0.01x^{2}+1})
integral of (x^2+1)^{-3/2}	\int\:(x^{2}+1)^{-\frac{3}{2}}dx
derivative of f(x)=x^4-4x^3	derivative\:f(x)=x^{4}-4x^{3}
integral of x*sqrt(1-x^4)	\int\:x\cdot\:\sqrt{1-x^{4}}dx
sum from n=0 to infinity of (1/2)^{n+1}	\sum\:_{n=0}^{\infty\:}(\frac{1}{2})^{n+1}
y^'+y/(x+1)=0	y^{\prime\:}+\frac{y}{x+1}=0
derivative of y=(8x^2+2x+8)/(sqrt(x))	derivative\:y=\frac{8x^{2}+2x+8}{\sqrt{x}}
derivative of x/(x^2+2)	derivative\:\frac{x}{x^{2}+2}
derivative of (e^{2x}-e^x+e^{-3x}/(e^x))	\frac{d}{dx}(\frac{e^{2x}-e^{x}+e^{-3x}}{e^{x}})
(\partial)/(\partial x)(2x)	\frac{\partial\:}{\partial\:x}(2x)
integral of 1/(x^2+1)	\int\:\frac{1}{x^{2}+1}dx
(\partial)/(\partial x)(zsin(x))	\frac{\partial\:}{\partial\:x}(z\sin(x))
derivative of ln(4x^2)	\frac{d}{dx}(\ln(4x^{2}))
area sin^2(x),sin^4(x),0,pi	area\:\sin^{2}(x),\sin^{4}(x),0,π
derivative of (sqrt(2)^x)	\frac{d}{dx}((\sqrt{2})^{x})
integral of cos(9x)sin(5x)	\int\:\cos(9x)\sin(5x)dx
y^3-(18x+6)+3xy^2(dy)/(dx)=0	y^{3}-(18x+6)+3xy^{2}\frac{dy}{dx}=0
derivative of ((1+sin(3x)/(3-2x))^{-1})	\frac{d}{dx}((\frac{1+\sin(3x)}{3-2x})^{-1})
sum from n=0 to infinity of (1+x)^n	\sum\:_{n=0}^{\infty\:}(1+x)^{n}
integral of 5x-x	\int\:5x-xdx
integral of \sqrt[5]{y^2}	\int\:\sqrt[5]{y^{2}}dy
derivative of (sqrt(1+x))/2	derivative\:\frac{\sqrt{1+x}}{2}
tangent of-2x^2,\at x=0	tangent\:-2x^{2},\at\:x=0
derivative of (sqrt(2)/(e^x+1/(e^x)))	\frac{d}{dx}(\frac{\sqrt{2}}{e^{x}+\frac{1}{e^{x}}})
integral of (sqrt(1-t^2))/(t^4)	\int\:\frac{\sqrt{1-t^{2}}}{t^{4}}dt
integral of 10ln(x^2-1)	\int\:10\ln(x^{2}-1)dx
tangent of (2x-6)/(x+1),\at x=0	tangent\:\frac{2x-6}{x+1},\at\:x=0
derivative of t/(sqrt(t^2+36))	derivative\:\frac{t}{\sqrt{t^{2}+36}}
y^{''}+y^'+4.25y=221cos(4.5t)	y^{\prime\:\prime\:}+y^{\prime\:}+4.25y=221\cos(4.5t)
integral from 0 to 4 of 1/(sqrt(4-x))	\int\:_{0}^{4}\frac{1}{\sqrt{4-x}}dx
derivative of (2x^3+8)/x	derivative\:\frac{2x^{3}+8}{x}
taylor 2/(1-x^2),0	taylor\:\frac{2}{1-x^{2}},0
integral of cos(x)cos(x)	\int\:\cos(x)\cos(x)dx
(\partial)/(\partial x)(sqrt(90-4x^2-1y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{90-4x^{2}-1y^{2}})
y^'=(t^2)/y (1+t^3)	y^{\prime\:}=\frac{t^{2}}{y}(1+t^{3})
integral from 0 to 13 of 8x	\int\:_{0}^{13}8xdx
(3x+ye^{y/x})dx-xe^{y/x}dy=0	(3x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0
-10x^2y+y^'=5x^2	-10x^{2}y+y^{\prime\:}=5x^{2}
limit as x approaches 5+of log_{3}(x-5)	\lim\:_{x\to\:5+}(\log_{3}(x-5))
limit as x approaches 0 of 4/(e^x+1)	\lim\:_{x\to\:0}(\frac{4}{e^{x}+1})
limit as x approaches 1 of ((1+x)(1-x)}{x*\frac{sin(pix))/x}	\lim\:_{x\to\:1}(\frac{(1+x)(1-x)}{x\cdot\:\frac{\sin(πx)}{x}})
integral of 1/(sqrt(x^2+6))	\int\:\frac{1}{\sqrt{x^{2}+6}}dx
(\partial)/(\partial x)((2x-3t)/(3x+5t))	\frac{\partial\:}{\partial\:x}(\frac{2x-3t}{3x+5t})
integral of 6/(x(ln(x))^2)	\int\:\frac{6}{x(\ln(x))^{2}}dx
derivative of 3t^2-3	derivative\:3t^{2}-3
integral of (sqrt(y^2-25))/(y^3)	\int\:\frac{\sqrt{y^{2}-25}}{y^{3}}dy

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