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Popular Calculus Problems

integral of 1-3/x	\int\:1-\frac{3}{x}dx
integral of ln(sqrt(x)+sqrt(x+1))	\int\:\ln(\sqrt{x}+\sqrt{x+1})dx
integral of xcos(21x)	\int\:x\cos(21x)dx
integral of x^2e^{-x^3}sin^2(x^3)	\int\:x^{2}e^{-x^{3}}\sin^{2}(x^{3})dx
(\partial)/(\partial x)(sin(y-5x))	\frac{\partial\:}{\partial\:x}(\sin(y-5x))
limit as x approaches pi/2 of sqrt(7e^{-2)}	\lim\:_{x\to\:\frac{π}{2}}(\sqrt{7e^{-2}})
integral of (4x)/(\sqrt[3]{5+3x^2)}	\int\:\frac{4x}{\sqrt[3]{5+3x^{2}}}dx
x^{''}+2x^'+2x=0,x(0)=0,x^'(0)=1	x^{\prime\:\prime\:}+2x^{\prime\:}+2x=0,x(0)=0,x^{\prime\:}(0)=1
integral of ((3x-1))/(sqrt(x^2-9))	\int\:\frac{(3x-1)}{\sqrt{x^{2}-9}}dx
sum from n=1 to infinity of 1/(2^n+2n)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}+2n}
integral of (x^3-27)/(x-3)	\int\:\frac{x^{3}-27}{x-3}dx
integral from 2 to 5 of 6sqrt(x)	\int\:_{2}^{5}6\sqrt{x}dx
y^'+2y=e^{-2t}	y^{\prime\:}+2y=e^{-2t}
limit as x approaches 0 of (e^x+x)^{2/x}	\lim\:_{x\to\:0}((e^{x}+x)^{\frac{2}{x}})
derivative of \sqrt[3]{x}*e^x	\frac{d}{dx}(\sqrt[3]{x}\cdot\:e^{x})
d/(dt)(sqrt(1-t^2))	\frac{d}{dt}(\sqrt{1-t^{2}})
(\partial)/(\partial x)(4/(xy))	\frac{\partial\:}{\partial\:x}(\frac{4}{xy})
(dy)/(dt)=e^{2(t)}-3y,y(0)=1	\frac{dy}{dt}=e^{2(t)}-3y,y(0)=1
integral from-1 to 0 of sqrt(3u+4)	\int\:_{-1}^{0}\sqrt{3u+4}du
integral of x^9sqrt(x^5+5)	\int\:x^{9}\sqrt{x^{5}+5}dx
derivative of y=(3+5x)^6(3x^7+2)^3	derivative\:y=(3+5x)^{6}(3x^{7}+2)^{3}
derivative of 7xsin(pix)	\frac{d}{dx}(7x\sin(πx))
derivative of (7x^2-14x+14e^x)	\frac{d}{dx}((7x^{2}-14x+14)e^{x})
integral of 1/((x-1)(x-2)(x-3))	\int\:\frac{1}{(x-1)(x-2)(x-3)}dx
derivative of-(30/(x^4))	\frac{d}{dx}(-\frac{30}{x^{4}})
integral of (1-2x^2+3x^3)	\int\:(1-2x^{2}+3x^{3})dx
integral of (ln(4x^2))/(sqrt(x))	\int\:\frac{\ln(4x^{2})}{\sqrt{x}}dx
integral of xe^{-x/(100)}	\int\:xe^{-\frac{x}{100}}dx
(\partial)/(\partial y)(9xy)	\frac{\partial\:}{\partial\:y}(9xy)
laplacetransform e^{-t}*sin(2t)	laplacetransform\:e^{-t}\cdot\:\sin(2t)
integral of (x^2)/(sqrt(x^2+6x+10))	\int\:\frac{x^{2}}{\sqrt{x^{2}+6x+10}}dx
limit as x approaches 0+of x^{14}ln(x)	\lim\:_{x\to\:0+}(x^{14}\ln(x))
f(x)=-sin(2x)*2	f(x)=-\sin(2x)\cdot\:2
(\partial)/(\partial y)(cos(2x-y))	\frac{\partial\:}{\partial\:y}(\cos(2x-y))
limit as x approaches 1 of x^2-4x+3	\lim\:_{x\to\:1}(x^{2}-4x+3)
integral of x/(e^{-x^2)}	\int\:\frac{x}{e^{-x^{2}}}dx
(\partial)/(\partial x)(2xln(y))	\frac{\partial\:}{\partial\:x}(2x\ln(y))
derivative of 2x^2-e^x	\frac{d}{dx}(2x^{2}-e^{x})
derivative of e^pi-e^{pix}+2pi^2	\frac{d}{dx}(e^{π}-e^{πx}+2π^{2})
y^{''}+2y=sin(sqrt(2)t)	y^{\prime\:\prime\:}+2y=\sin(\sqrt{2}t)
derivative of tan(4x)	derivative\:\tan(4x)
taylor e^{5x},0	taylor\:e^{5x},0
integral of 5/(x^2-10x)	\int\:\frac{5}{x^{2}-10x}dx
integral of 1/(sqrt(3-2x^2))	\int\:\frac{1}{\sqrt{3-2x^{2}}}dx
derivative of e^tcos(4t)	derivative\:e^{t}\cos(4t)
integral of x^{5/2}ln(x)	\int\:x^{\frac{5}{2}}\ln(x)dx
(\partial)/(\partial x)((3x-2x^2)^3)	\frac{\partial\:}{\partial\:x}((3x-2x^{2})^{3})
integral of ((1+x)/x)^2	\int\:(\frac{1+x}{x})^{2}dx
(dy)/(dx)= 1/(y^2)	\frac{dy}{dx}=\frac{1}{y^{2}}
tangent of f(x)=3x-12x^3,\at x=0	tangent\:f(x)=3x-12x^{3},\at\:x=0
integral of 4xsqrt(1+4x^2)	\int\:4x\sqrt{1+4x^{2}}dx
derivative of f(x)=4x^2e^{2x^2+x-1}	derivative\:f(x)=4x^{2}e^{2x^{2}+x-1}
integral of 13-(x/(40))	\int\:13-(\frac{x}{40})dx
integral of x^2ln(6x)	\int\:x^{2}\ln(6x)dx
derivative of 8/(\sqrt[5]{x)}	derivative\:\frac{8}{\sqrt[5]{x}}
integral of 3x^2+4x-1	\int\:3x^{2}+4x-1dx
derivative of sqrt(x)y	\frac{d}{dx}(\sqrt{x}y)
(4x+ye^{y/x})dx-xe^{y/x}dy=0	(4x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0
derivative of (e^{-x})(x^2-x)	derivative\:(e^{-x})(x^{2}-x)
integral of ((x^2))/(sqrt(9+x^2))	\int\:\frac{(x^{2})}{\sqrt{9+x^{2}}}dx
integral of 10\sqrt[3]{x^2}	\int\:10\sqrt[3]{x^{2}}dx
derivative of 1/((1-x))	derivative\:\frac{1}{(1-x)}
tangent of sqrt(3x+7)	tangent\:\sqrt{3x+7}
(\partial)/(\partial x)(-e^xsin(y))	\frac{\partial\:}{\partial\:x}(-e^{x}\sin(y))
derivative of e^xsin(6x)	\frac{d}{dx}(e^{x}\sin(6x))
normal of y=(-4)+x^2,(1,-3)	normal\:y=(-4)+x^{2},(1,-3)
integral of x^2sqrt(x+3)	\int\:x^{2}\sqrt{x+3}dx
taylor cos(2x)	taylor\:\cos(2x)
(\partial)/(\partial z)(x^2+2y+2z)	\frac{\partial\:}{\partial\:z}(x^{2}+2y+2z)
derivative of 7/(x^4)	\frac{d}{dx}(\frac{7}{x^{4}})
limit as x approaches 0 of-2csc(2x)	\lim\:_{x\to\:0}(-2\csc(2x))
(\partial)/(\partial x)(-sin(x))	\frac{\partial\:}{\partial\:x}(-\sin(x))
derivative of (1-x/(2x))	\frac{d}{dx}(\frac{1-x}{2x})
sum from n=1 to infinity of (-1)^n 1/n	\sum\:_{n=1}^{\infty\:}(-1)^{n}\frac{1}{n}
derivative of (-u^2+8)/((u^2+8)^2)	derivative\:\frac{-u^{2}+8}{(u^{2}+8)^{2}}
f(x)=e^xcosh(x)	f(x)=e^{x}\cosh(x)
x^2y^{''}-11xy^'+36y=0	x^{2}y^{\prime\:\prime\:}-11xy^{\prime\:}+36y=0
derivative of xln(x^2+x)	\frac{d}{dx}(x\ln(x^{2}+x))
integral of (e^{2t})/2	\int\:\frac{e^{2t}}{2}dt
limit as x approaches pi/2+of cos(x)	\lim\:_{x\to\:\frac{π}{2}+}(\cos(x))
integral of (4/x-1)	\int\:(\frac{4}{x}-1)dx
(\partial)/(\partial x)(xsin(4x^2y))	\frac{\partial\:}{\partial\:x}(x\sin(4x^{2}y))
y^'=(2x)/((1+2y))	y^{\prime\:}=\frac{2x}{(1+2y)}
integral of x/(sqrt(x^4-6x^2+5))	\int\:\frac{x}{\sqrt{x^{4}-6x^{2}+5}}dx
derivative of log_{3}(x^2+1)	\frac{d}{dx}(\log_{3}(x^{2}+1))
derivative of (x+1/x ^2)	\frac{d}{dx}((x+\frac{1}{x})^{2})
d/(dt)((t-2)^2)	\frac{d}{dt}((t-2)^{2})
(\partial)/(\partial x)(yx+y)	\frac{\partial\:}{\partial\:x}(yx+y)
integral from 6 to 3 of (9x^2-4x+9)	\int\:_{6}^{3}(9x^{2}-4x+9)dx
integral of (-x-3)/(x^3-x)	\int\:\frac{-x-3}{x^{3}-x}dx
integral of (2x+3)/(x(x+1)(x-1))	\int\:\frac{2x+3}{x(x+1)(x-1)}dx
(\partial)/(\partial x)((x+y)/(z-2y))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{z-2y})
integral of (cos(x))/(4-sin(x))	\int\:\frac{\cos(x)}{4-\sin(x)}dx
integral from 1 to 4 of xf(x)	\int\:_{1}^{4}xf(x)dx
integral of (x^2+4)/(x^2)	\int\:\frac{x^{2}+4}{x^{2}}dx
integral of xarctan(sqrt(x^2-1))	\int\:x\arctan(\sqrt{x^{2}-1})dx
integral of sqrt((x-1)/(x+1))	\int\:\sqrt{\frac{x-1}{x+1}}dx
derivative of e^{-x}	derivative\:e^{-x}
maclaurin 5cos(pix)	maclaurin\:5\cos(πx)
derivative of-(2x/((-x^2+1)^2))	\frac{d}{dx}(-\frac{2x}{(-x^{2}+1)^{2}})

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