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Popular Calculus Problems

integral of ((3x^2+4))/((x^2-2x+2)^2)	\int\:\frac{(3x^{2}+4)}{(x^{2}-2x+2)^{2}}dx
integral of 8x(x^7-1/8)	\int\:8x(x^{7}-\frac{1}{8})dx
limit as x approaches pi/3 of sin(x)	\lim\:_{x\to\:\frac{π}{3}}(\sin(x))
derivative of x^2a+a^2b+b^2x	\frac{d}{dx}(x^{2}a+a^{2}b+b^{2}x)
integral of csc^4(6w)	\int\:\csc^{4}(6w)dw
integral from 0 to e of 4e^{2x}	\int\:_{0}^{e}4e^{2x}dx
integral of-2x+15x^2-4x^3+C	\int\:-2x+15x^{2}-4x^{3}+Cdx
y^'+((7x)/(x^2+1))y=(7x)/(x^2+1)	y^{\prime\:}+(\frac{7x}{x^{2}+1})y=\frac{7x}{x^{2}+1}
derivative of (((4/x)^2))/(1-4/x)	derivative\:\frac{((\frac{4}{x})^{2})}{1-\frac{4}{x}}
derivative of sqrt(4+\sqrt{7x)}	\frac{d}{dx}(\sqrt{4+\sqrt{7x}})
integral from 0 to 1 of 5^{4x}	\int\:_{0}^{1}5^{4x}dx
(\partial)/(\partial x)(ysin(2x))	\frac{\partial\:}{\partial\:x}(y\sin(2x))
limit as x approaches 0+of 1/(ln(x))	\lim\:_{x\to\:0+}(\frac{1}{\ln(x)})
xyy^'=2y^2+4x^2	xyy^{\prime\:}=2y^{2}+4x^{2}
limit as x approaches x of tan(x)	\lim\:_{x\to\:x}(\tan(x))
inverse oflaplace 4/((s-4)^3)	inverselaplace\:\frac{4}{(s-4)^{3}}
(\partial)/(\partial x)(3cos(2x))	\frac{\partial\:}{\partial\:x}(3\cos(2x))
derivative of h(x)= 1/(x^2)+1/x+x	derivative\:h(x)=\frac{1}{x^{2}}+\frac{1}{x}+x
integral of (cos(ax))/(sqrt(b-asin(ax)))	\int\:\frac{\cos(ax)}{\sqrt{b-a\sin(ax)}}dx
limit as x approaches 5 of 3x+6	\lim\:_{x\to\:5}(3x+6)
derivative of arcsin(sqrt(x/(1-x)))	\frac{d}{dx}(\arcsin(\sqrt{\frac{x}{1-x}}))
integral of x/(x^2)	\int\:\frac{x}{x^{2}}dx
integral of (sin(sqrt(x+1)))/(sqrt(x+1))	\int\:\frac{\sin(\sqrt{x+1})}{\sqrt{x+1}}dx
integral from 1 to e of (ln(x))/x	\int\:_{1}^{e}\frac{\ln(x)}{x}dx
derivative of (1+6x^2)(x-x^2)	derivative\:(1+6x^{2})(x-x^{2})
limit as x approaches infinity of-3x^2	\lim\:_{x\to\:\infty\:}(-3x^{2})
y^{''}-2y^'-3y=0,y(0)=b,y^'(0)=2	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=0,y(0)=b,y^{\prime\:}(0)=2
(\partial)/(\partial x)(cos(2(2yx-1)))	\frac{\partial\:}{\partial\:x}(\cos(2(2yx-1)))
(\partial)/(\partial x)(e^{xyz-2})	\frac{\partial\:}{\partial\:x}(e^{xyz-2})
limit as x approaches 0+of 2/(x^{1/3)}	\lim\:_{x\to\:0+}(\frac{2}{x^{\frac{1}{3}}})
derivative of sin^2(pix)	derivative\:\sin^{2}(πx)
(\partial)/(\partial x)(98y^2+x^2-x^2y)	\frac{\partial\:}{\partial\:x}(98y^{2}+x^{2}-x^{2}y)
derivative of (x-4^2-5)	\frac{d}{dx}((x-4)^{2}-5)
sum from n=0 to infinity of ne^{-n^2}	\sum\:_{n=0}^{\infty\:}ne^{-n^{2}}
derivative of f(x)=(1+3x^2)(x-x^2)	derivative\:f(x)=(1+3x^{2})(x-x^{2})
y^'+2y=te^{-2t},y(1)=0	y^{\prime\:}+2y=te^{-2t},y(1)=0
integral of [(3-x^2)^3]	\int\:[(3-x^{2})^{3}]dx
integral of (-3)/((x-2)(x^2+4))	\int\:\frac{-3}{(x-2)(x^{2}+4)}dx
limit as x approaches 2+of 2	\lim\:_{x\to\:2+}(2)
derivative of (3x+5^7)	\frac{d}{dx}((3x+5)^{7})
integral from-1 to 0 of (2x-e^x)	\int\:_{-1}^{0}(2x-e^{x})dx
derivative of ln(-x^2+6x)	\frac{d}{dx}(\ln(-x^{2}+6x))
integral of-2sin(2x+5)	\int\:-2\sin(2x+5)dx
(\partial)/(\partial y)(xy^2z^2)	\frac{\partial\:}{\partial\:y}(xy^{2}z^{2})
derivative of 3/(x^3+x^{-4})	\frac{d}{dx}(\frac{3}{x^{3}}+x^{-4})
integral of (x^3)/(1-9x^2)	\int\:\frac{x^{3}}{1-9x^{2}}dx
derivative of y=(x+7)/(5x^2e^x)	derivative\:y=\frac{x+7}{5x^{2}e^{x}}
integral of (4/x+e^{2x})	\int\:(\frac{4}{x}+e^{2x})dx
integral of sec(x)sec^2(x)	\int\:\sec(x)\sec^{2}(x)dx
integral of xcos(pi*x)	\int\:x\cos(π\cdot\:x)dx
derivative of 2x-2^{-x}	\frac{d}{dx}(2x-2^{-x})
limit as x approaches 2 of (x^2-6)/(x-3)	\lim\:_{x\to\:2}(\frac{x^{2}-6}{x-3})
derivative of 1+ln^2(x)	\frac{d}{dx}(1+\ln^{2}(x))
(\partial)/(\partial x)(tan(2x))	\frac{\partial\:}{\partial\:x}(\tan(2x))
integral from 0 to 1 of 2pix(x-x^3)	\int\:_{0}^{1}2πx(x-x^{3})dx
derivative of 2x^2+2	\frac{d}{dx}(2x^{2}+2)
derivative of (2x^9-5x+sqrt(x)/(x^4))	\frac{d}{dx}(\frac{2x^{9}-5x+\sqrt{x}}{x^{4}})
integral from 0 to r of 0	\int\:_{0}^{r}0dr
integral of 5/((x-2)(x^2+4))	\int\:\frac{5}{(x-2)(x^{2}+4)}dx
integral of x^2In	\int\:x^{2}Indx
derivative of log_{a}(x)	derivative\:\log_{a}(x)
sum from n=3 to infinity of 2/(n^2-2n)	\sum\:_{n=3}^{\infty\:}\frac{2}{n^{2}-2n}
(\partial)/(\partial y)(-x-y)	\frac{\partial\:}{\partial\:y}(-x-y)
limit as x approaches-infinity of e^{3x}	\lim\:_{x\to\:-\infty\:}(e^{3x})
y^'-7/x y=(y^4)/(x^5)	y^{\prime\:}-\frac{7}{x}y=\frac{y^{4}}{x^{5}}
xydy+e^{-x}(y^2-1)dx=0	xydy+e^{-x}(y^{2}-1)dx=0
y^'=((y-x))/((x))	y^{\prime\:}=\frac{(y-x)}{(x)}
(dy)/(dx)=(x^2)/(x^2+1)	\frac{dy}{dx}=\frac{x^{2}}{x^{2}+1}
integral of 2+3x-4y^3	\int\:2+3x-4y^{3}dx
integral from 0 to 9 of pi(2sqrt(3y))^2	\int\:_{0}^{9}π(2\sqrt{3y})^{2}dy
derivative of x^3+2x-5	\frac{d}{dx}(x^{3}+2x-5)
limit as x approaches 4 of (2x-1)/(x-4)	\lim\:_{x\to\:4}(\frac{2x-1}{x-4})
integral of 5xe^{-x}	\int\:5xe^{-x}dx
derivative of y=(x^2+1)^2	derivative\:y=(x^{2}+1)^{2}
tangent of xy=-64,(8,-8)	tangent\:xy=-64,(8,-8)
integral of 1/(10^x+1)	\int\:\frac{1}{10^{x}+1}dx
derivative of 10cos(30x-7)	\frac{d}{dx}(10\cos(30x-7))
integral of csch^2(13x-4/9)	\int\:\csch^{2}(13x-\frac{4}{9})dx
slope of (-1,-1),(4,-6)	slope\:(-1,-1),(4,-6)
derivative of 6sqrt(t^5)	derivative\:6\sqrt{t^{5}}
derivative of (1+sqrt(t))(8t^2-1)	derivative\:(1+\sqrt{t})(8t^{2}-1)
limit as x approaches infinity of 3x^4	\lim\:_{x\to\:\infty\:}(3x^{4})
limit as x approaches 0 of (e^x-1)/(7x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{7x})
(\partial)/(\partial x)(-5e^{-5y}sin(5x))	\frac{\partial\:}{\partial\:x}(-5e^{-5y}\sin(5x))
limit as x approaches 2 of 2-x	\lim\:_{x\to\:2}(2-x)
d/(dt)(2/(2-cos(pit)))	\frac{d}{dt}(\frac{2}{2-\cos(πt)})
derivative of 2e^{cos(x/2})	\frac{d}{dx}(2e^{\cos(\frac{x}{2})})
derivative of ((x^2-3x))/(x+1)	derivative\:\frac{(x^{2}-3x)}{x+1}
integral of (2x+1)/(x^2-x-6)	\int\:\frac{2x+1}{x^{2}-x-6}dx
integral of 4sech(x)tanh(x)	\int\:4\sech(x)\tanh(x)dx
limit as x approaches 0 of 2x^3	\lim\:_{x\to\:0}(2x^{3})
(dy)/(dx)=1+x-y-xy	\frac{dy}{dx}=1+x-y-xy
integral of 1/60 x^3	\int\:\frac{1}{60}x^{3}dx
integral of-9sec(x)tan(x)-2sec^2(x)	\int\:-9\sec(x)\tan(x)-2\sec^{2}(x)dx
(\partial)/(\partial x)(e^x-e^{-x})	\frac{\partial\:}{\partial\:x}(e^{x}-e^{-x})
derivative of 1-1/(2x)	\frac{d}{dx}(1-\frac{1}{2x})
(dy}{dx}=\frac{x-1)/y	\frac{dy}{dx}=\frac{x-1}{y}
integral of (x^2)/(sqrt(x^2-16))	\int\:\frac{x^{2}}{\sqrt{x^{2}-16}}dx
integral of 1/((a+bx)^3)	\int\:\frac{1}{(a+bx)^{3}}dx
integral from 0 to 0.5 of (300x)	\int\:_{0}^{0.5}(300x)dx

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