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Popular Calculus Problems

integral from 0 to 1 of xsin(x^2)	\int\:_{0}^{1}x\sin(x^{2})dx
integral of (x^4+3x)^2	\int\:(x^{4}+3x)^{2}dx
limit as x approaches 1 of x^3+x^2-3	\lim\:_{x\to\:1}(x^{3}+x^{2}-3)
integral from 1 to 32 of (x^{-6/5})	\int\:_{1}^{32}(x^{-\frac{6}{5}})dx
tangent of f(x)=sqrt(3x+13),(12,7)	tangent\:f(x)=\sqrt{3x+13},(12,7)
derivative of y=3(ln(x)+1)	derivative\:y=3(\ln(x)+1)
derivative of 2cos(5x)	\frac{d}{dx}(2\cos(5x))
limit as h approaches 0 of (1+h/y)^{1/h}	\lim\:_{h\to\:0}((1+\frac{h}{y})^{\frac{1}{h}})
integral of (sqrt(2)+1/(sqrt(x)))^2	\int\:(\sqrt{2}+\frac{1}{\sqrt{x}})^{2}dx
sum from n=1 to infinity of (2/5)^n	\sum\:_{n=1}^{\infty\:}(\frac{2}{5})^{n}
derivative of (sin(x^2))/(3x)	derivative\:\frac{\sin(x^{2})}{3x}
derivative of (1+sqrt(x))/(1-sqrt(x))	derivative\:\frac{1+\sqrt{x}}{1-\sqrt{x}}
sum from n=0 to infinity of 1/(e^{2n)}	\sum\:_{n=0}^{\infty\:}\frac{1}{e^{2n}}
integral of (2x-1)^{1/2}	\int\:(2x-1)^{\frac{1}{2}}dx
(\partial)/(\partial x)(-y)	\frac{\partial\:}{\partial\:x}(-y)
derivative of (7x+3)^2	derivative\:(7x+3)^{2}
y^{''}-4y^'+3y=2cos(3t)	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=2\cos(3t)
slope of f(x)=(2x-x^2)/(4x^2+1)	slope\:f(x)=\frac{2x-x^{2}}{4x^{2}+1}
derivative of 4/(7x^3)	\frac{d}{dx}(\frac{4}{7x^{3}})
derivative of (6x^{6x})	\frac{d}{dx}((6x)^{6x})
y^'+y+3sin(x)=0	y^{\prime\:}+y+3\sin(x)=0
area y=x^2-14,y=7-4x	area\:y=x^{2}-14,y=7-4x
derivative of 1/(x^{13})	\frac{d}{dx}(\frac{1}{x^{13}})
integral of sqrt(x^2-2x)	\int\:\sqrt{x^{2}-2x}dx
inverse oflaplace 1/(s(s+2)^2)	inverselaplace\:\frac{1}{s(s+2)^{2}}
y^{''}=-9y	y^{\prime\:\prime\:}=-9y
taylor xln(7x),1	taylor\:x\ln(7x),1
integral of (4ln(x))/(x^3)	\int\:\frac{4\ln(x)}{x^{3}}dx
derivative of f(x)=(c^4-x^4)/(c^4+x^4)	derivative\:f(x)=\frac{c^{4}-x^{4}}{c^{4}+x^{4}}
d/(dy)(y^{-2})	\frac{d}{dy}(y^{-2})
integral from-1 to 1 of e^x-x^2+1	\int\:_{-1}^{1}e^{x}-x^{2}+1dx
integral of (x^2)/(x^2+x^4)	\int\:\frac{x^{2}}{x^{2}+x^{4}}dx
integral from 0 to 1 of 5cos((pit)/2)	\int\:_{0}^{1}5\cos(\frac{πt}{2})dt
y^{''}-4y^'=16t	y^{\prime\:\prime\:}-4y^{\prime\:}=16t
integral of 1/((a+bx)^{1/3)}	\int\:\frac{1}{(a+bx)^{\frac{1}{3}}}dx
x^2ydx+x^3dy=0	x^{2}ydx+x^{3}dy=0
limit as x approaches-2 of-2x^3-3x^2+8	\lim\:_{x\to\:-2}(-2x^{3}-3x^{2}+8)
integral of 0.1e^{0.4x}	\int\:0.1e^{0.4x}dx
y^{'''}+5y^{''}+7y^'-13y=0	y^{\prime\:\prime\:\prime\:}+5y^{\prime\:\prime\:}+7y^{\prime\:}-13y=0
derivative of (x^2+2x-1-(2x^2-3x+6))	\frac{d}{dx}((x^{2}+2x-1)-(2x^{2}-3x+6))
integral of 1/((t^2+1)^{3/2)}	\int\:\frac{1}{(t^{2}+1)^{\frac{3}{2}}}dt
(dy)/(dx)=(x+y-2)^2	\frac{dy}{dx}=(x+y-2)^{2}
(d^2)/(dx^2)(sqrt(3x-7))	\frac{d^{2}}{dx^{2}}(\sqrt{3x-7})
area 2x^2+5x+6,(-2,0)	area\:2x^{2}+5x+6,(-2,0)
limit as x approaches infinity of-1^x	\lim\:_{x\to\:\infty\:}(-1^{x})
derivative of (sin(x)^{-1})	\frac{d}{dx}((\sin(x))^{-1})
limit as x approaches-infinity of (x^3+1)/(x^2-1)	\lim\:_{x\to\:-\infty\:}(\frac{x^{3}+1}{x^{2}-1})
taylor 1/((1-x)^2)	taylor\:\frac{1}{(1-x)^{2}}
integral of (3cos(ln(x)))/x	\int\:\frac{3\cos(\ln(x))}{x}dx
derivative of arctan(4^x)	\frac{d}{dx}(\arctan(4^{x}))
derivative of ln(x-2+(x-3)/(x-2))	\frac{d}{dx}(\ln(x-2)+\frac{x-3}{x-2})
derivative of sqrt(6x+1)	derivative\:\sqrt{6x+1}
integral of ((-2cos(x)))/(sin^2(x))	\int\:\frac{(-2\cos(x))}{\sin^{2}(x)}dx
derivative of (\sqrt[3]{x})/4	derivative\:\frac{\sqrt[3]{x}}{4}
integral of 1/(sqrt(25x^2-49))	\int\:\frac{1}{\sqrt{25x^{2}-49}}dx
integral of (6-x)/(sqrt(4x^2-12x+7))	\int\:\frac{6-x}{\sqrt{4x^{2}-12x+7}}dx
ty^'+3y=t^2-t+7	ty^{\prime\:}+3y=t^{2}-t+7
limit as x approaches 0 of sqrt(1/x)	\lim\:_{x\to\:0}(\sqrt{\frac{1}{x}})
limit as x approaches 2 of x^3-4x	\lim\:_{x\to\:2}(x^{3}-4x)
tangent of f(x)=x^2-5x	tangent\:f(x)=x^{2}-5x
limit as x approaches 0 of 1/x+3	\lim\:_{x\to\:0}(\frac{1}{x}+3)
derivative of e^{(x+y})	\frac{d}{dx}(e^{(x+y)})
derivative of arcsin(ax)	\frac{d}{dx}(\arcsin(ax))
derivative of ((x+9))/((x+4))	derivative\:\frac{(x+9)}{(x+4)}
area 3sin(x),0,0.6pi,4cos(x)	area\:3\sin(x),0,0.6π,4\cos(x)
y^{''}+9y=e^{-t}	y^{\prime\:\prime\:}+9y=e^{-t}
integral of arcsin(cos(x))	\int\:\arcsin(\cos(x))dx
integral of 1/((16+x^2)^2)	\int\:\frac{1}{(16+x^{2})^{2}}dx
integral from 0 to infinity of 8e^{-8x}	\int\:_{0}^{\infty\:}8e^{-8x}dx
limit as y approaches 1 of (y-1)/(y^6-1)	\lim\:_{y\to\:1}(\frac{y-1}{y^{6}-1})
derivative of ln(2x+3)	derivative\:\ln(2x+3)
derivative of 8/(sin(x)+1/(cot(x)))	\frac{d}{dx}(\frac{8}{\sin(x)}+\frac{1}{\cot(x)})
integral from 0 to pi/2 of cos^2(2x)	\int\:_{0}^{\frac{π}{2}}\cos^{2}(2x)dx
derivative of sin^4(x/4)+cos^4(x/4)	derivative\:\sin^{4}(\frac{x}{4})+\cos^{4}(\frac{x}{4})
(\partial)/(\partial x)(xy+y+2x+2)	\frac{\partial\:}{\partial\:x}(xy+y+2x+2)
f(θ)=θcos(θ)sin(θ)	f(θ)=θ\cos(θ)\sin(θ)
(\partial)/(\partial y)(y^2-4y+xy)	\frac{\partial\:}{\partial\:y}(y^{2}-4y+xy)
integral of (4x^2-9x)^5(8x-9)	\int\:(4x^{2}-9x)^{5}(8x-9)dx
limit as x approaches 0 of (sin^3(x))/(x^2)	\lim\:_{x\to\:0}(\frac{\sin^{3}(x)}{x^{2}})
sum from n=1 to infinity of n/(e^{4n)}	\sum\:_{n=1}^{\infty\:}\frac{n}{e^{4n}}
integral of (2x^2-5x+2)/(x^3+x)	\int\:\frac{2x^{2}-5x+2}{x^{3}+x}dx
derivative of (-2/((x-1)^3))	\frac{d}{dx}(\frac{-2}{(x-1)^{3}})
integral of (1-2sqrt(x))^{2021}	\int\:(1-2\sqrt{x})^{2021}dx
limit as x approaches+4+of ln(x-4)	\lim\:_{x\to\:+4+}(\ln(x-4))
taylor 1/((1-x)^3),0	taylor\:\frac{1}{(1-x)^{3}},0
integral of 2/(sqrt(x+2)+\sqrt{x)}	\int\:\frac{2}{\sqrt{x+2}+\sqrt{x}}dx
derivative of e^9	derivative\:e^{9}
integral of 3x+2y	\int\:3x+2ydy
y^{''}-8y^'=64t,y(0)=8,y^'(0)=0	y^{\prime\:\prime\:}-8y^{\prime\:}=64t,y(0)=8,y^{\prime\:}(0)=0
integral of (x^3)/(2x+1)	\int\:\frac{x^{3}}{2x+1}dx
derivative of ln(ax^2+b)	\frac{d}{dx}(\ln(ax^{2}+b))
limit as y approaches 1 of 85	\lim\:_{y\to\:1}(85)
d/(dy)(2e^{xy^2})	\frac{d}{dy}(2e^{xy^{2}})
y^'=3y+x	y^{\prime\:}=3y+x
derivative of f(x)= x/(1+x)	derivative\:f(x)=\frac{x}{1+x}
sum from n=0 to infinity of (e^n+5)/(e^{2n)}	\sum\:_{n=0}^{\infty\:}\frac{e^{n}+5}{e^{2n}}
derivative of 4x^2sin(xtan(x))	\frac{d}{dx}(4x^{2}\sin(x)\tan(x))
integral of (cos^2(x))	\int\:(\cos^{2}(x))dx
integral of x+5cos(x)	\int\:x+5\cos(x)dx
integral of (csc^5(ln(x)))/x	\int\:\frac{\csc^{5}(\ln(x))}{x}dx

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