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Popular Calculus Problems

sum from n=1 to infinity of (0.2)^n	\sum\:_{n=1}^{\infty\:}(0.2)^{n}
integral from pi/2 to pi of cos^2(x)	\int\:_{\frac{π}{2}}^{π}\cos^{2}(x)dx
2y^{''}+18y=0	2y^{\prime\:\prime\:}+18y=0
integral of x/((3-x^2)^6)	\int\:\frac{x}{(3-x^{2})^{6}}dx
(\partial)/(\partial x)(5+xln(xy-5))	\frac{\partial\:}{\partial\:x}(5+x\ln(xy-5))
y^'-xy^'=2xy	y^{\prime\:}-xy^{\prime\:}=2xy
integral of (y^2e^{xy}+cos(x))	\int\:(y^{2}e^{xy}+\cos(x))dx
derivative of 5x-4	derivative\:5x-4
integral of y/(y+6)	\int\:\frac{y}{y+6}dy
integral of 2x(x^2-1)^2	\int\:2x(x^{2}-1)^{2}dx
area x=20-5y^2,x=5y^2-20	area\:x=20-5y^{2},x=5y^{2}-20
limit as x approaches 3 of 3/(9-x^2)	\lim\:_{x\to\:3}(\frac{3}{9-x^{2}})
area y=xsqrt(4-x^2),(2,-2)	area\:y=x\sqrt{4-x^{2}},(2,-2)
derivative of \sqrt[8]{t}-8e^t	derivative\:\sqrt[8]{t}-8e^{t}
derivative of (cos(4x)^x)	\frac{d}{dx}((\cos(4x))^{x})
derivative of sin^3(x^3)	\frac{d}{dx}(\sin^{3}(x^{3}))
derivative of ((x+2)/(x-2))^5	derivative\:(\frac{x+2}{x-2})^{5}
derivative of f(1)=2x^3	derivative\:f(1)=2x^{3}
inverse oflaplace 1/(s^3(s+1))	inverselaplace\:\frac{1}{s^{3}(s+1)}
integral of 0.06x-0.6-(7700)/(x^2)	\int\:0.06x-0.6-\frac{7700}{x^{2}}dx
integral from-1 to 1 of 12^x	\int\:_{-1}^{1}12^{x}dx
(d^2)/(dx^2)(x/(x^2-1))	\frac{d^{2}}{dx^{2}}(\frac{x}{x^{2}-1})
y^{''}+(8)y=0	y^{\prime\:\prime\:}+(8)y=0
limit as h approaches+0 of ((2^h-1))/h	\lim\:_{h\to\:+0}(\frac{(2^{h}-1)}{h})
sum from n=0 to infinity of 100	\sum\:_{n=0}^{\infty\:}100
y^{''}-2y^'+y=x^2	y^{\prime\:\prime\:}-2y^{\prime\:}+y=x^{2}
(\partial)/(\partial x)(x^3-5xy)	\frac{\partial\:}{\partial\:x}(x^{3}-5xy)
(xdy)/(dx)+(3x+1)y=e^{-3x}	\frac{xdy}{dx}+(3x+1)y=e^{-3x}
derivative of \sqrt[5]{(x^2+x/(x+1)})	\frac{d}{dx}(\sqrt[5]{\frac{x^{2}+x}{x+1}})
integral of (8x)/((2x^2+5)^4)	\int\:\frac{8x}{(2x^{2}+5)^{4}}dx
limit as x approaches 0 of (sin(5x))/(tan(6x))	\lim\:_{x\to\:0}(\frac{\sin(5x)}{\tan(6x)})
integral of 1/(x(4-ln^2(x)))	\int\:\frac{1}{x(4-\ln^{2}(x))}dx
derivative of f(x)=(-9x)/(sqrt(2x-1))	derivative\:f(x)=\frac{-9x}{\sqrt{2x-1}}
integral of (cos^3(x))/(1-sin(x))	\int\:\frac{\cos^{3}(x)}{1-\sin(x)}dx
derivative of sexx	\frac{d}{dx}(sexx)
integral from-1 to-0.5 of 1.5x^2	\int\:_{-1}^{-0.5}1.5x^{2}dx
(1-x^2)y^{''}-xy^'+y=0	(1-x^{2})y^{\prime\:\prime\:}-xy^{\prime\:}+y=0
limit as x approaches 0 of (x^2-4)/x	\lim\:_{x\to\:0}(\frac{x^{2}-4}{x})
area x^4-4x^2,x^2-4	area\:x^{4}-4x^{2},x^{2}-4
derivative of y=ln(x^2sqrt(x+1))	derivative\:y=\ln(x^{2}\sqrt{x+1})
limit as x approaches 8-of 1/(x-8)	\lim\:_{x\to\:8-}(\frac{1}{x-8})
limit as x approaches 2+of x/(4-x^2)	\lim\:_{x\to\:2+}(\frac{x}{4-x^{2}})
integral of x/(x^4+2x^2+2)	\int\:\frac{x}{x^{4}+2x^{2}+2}dx
limit as x approaches 2pi-of (x)csc(x)	\lim\:_{x\to\:2π-}((x)\csc(x))
inverse oflaplace {((s+1)^3)/(s^4)}	inverselaplace\:\left\{\frac{(s+1)^{3}}{s^{4}}\right\}
limit as h approaches 0 of x+h	\lim\:_{h\to\:0}(x+h)
(\partial)/(\partial x)(e^{3x}*tan(y))	\frac{\partial\:}{\partial\:x}(e^{3x}\cdot\:\tan(y))
(\partial)/(\partial x)(4xy^8+x^3y^2)	\frac{\partial\:}{\partial\:x}(4xy^{8}+x^{3}y^{2})
(\partial)/(\partial x)(5xy-2x^2y)	\frac{\partial\:}{\partial\:x}(5xy-2x^{2}y)
integral of 1/(4+x^2)	\int\:\frac{1}{4+x^{2}}dx
derivative of f(x)=2xln(3x)-2x	derivative\:f(x)=2x\ln(3x)-2x
integral of (x-1)^2x^3(2-x)	\int\:(x-1)^{2}x^{3}(2-x)dx
limit as x approaches-infinity of 4/x-12	\lim\:_{x\to\:-\infty\:}(\frac{4}{x}-12)
derivative of 2sec^2(x*tan(x))	\frac{d}{dx}(2\sec^{2}(x)\cdot\:\tan(x))
xdx+(x^2y+4y)dy=0	xdx+(x^{2}y+4y)dy=0
y^'+5y=2	y^{\prime\:}+5y=2
integral of ((sqrt(x)-1)^3)/(sqrt(x))	\int\:\frac{(\sqrt{x}-1)^{3}}{\sqrt{x}}dx
derivative of A(e^{2x}+2e^{2x}x)	\frac{d}{dx}(A(e^{2x}+2e^{2x}x))
derivative of-2cot(x+6x^4csc(x))	\frac{d}{dx}(-2\cot(x)+6x^{4}\csc(x))
derivative of f(x)=x^{1/9}	derivative\:f(x)=x^{\frac{1}{9}}
derivative of sqrt(8-5x)	\frac{d}{dx}(\sqrt{8-5x})
derivative of ((x^2+3/(x^2-3))^3)	\frac{d}{dx}((\frac{x^{2}+3}{x^{2}-3})^{3})
integral of (2x^3+x)(x^4+x^2)^{108}	\int\:(2x^{3}+x)(x^{4}+x^{2})^{108}dx
f(x)=sin(9x)	f(x)=\sin(9x)
derivative of 500x-2x^2	\frac{d}{dx}(500x-2x^{2})
x(dy)/(dx)=2xe^x-y+6x^2	x\frac{dy}{dx}=2xe^{x}-y+6x^{2}
derivative of (24/(x^2+4x))	\frac{d}{dx}(\frac{24}{x^{2}+4x})
laplacetransform sin(2t)sin(t)	laplacetransform\:\sin(2t)\sin(t)
integral of nxe^{nθ}e^{-xn}	\int\:nxe^{nθ}e^{-xn}dx
(\partial}{\partial x}(\frac{432)/y+3y)	\frac{\partial\:}{\partial\:x}(\frac{432}{y}+3y)
derivative of sqrt(x^3-1)	\frac{d}{dx}(\sqrt{x^{3}-1})
integral from-infinity to-1 of x^{-16/7}	\int\:_{-\infty\:}^{-1}x^{-\frac{16}{7}}dx
integral of csc(t/4)cot(t/4)	\int\:\csc(\frac{t}{4})\cot(\frac{t}{4})dt
integral of tan^3(t)sec^2(t)	\int\:\tan^{3}(t)\sec^{2}(t)dt
derivative of (x^2)/((1+x))	derivative\:\frac{x^{2}}{(1+x)}
inverse oflaplace s/((s+1)^2)	inverselaplace\:\frac{s}{(s+1)^{2}}
d/(d{z)}(({x})/(({x)^2+{y}^2+{z}^2)^{3/2}})	\frac{d}{d{z}}(\frac{{x}}{({x}^{2}+{y}^{2}+{z}^{2})^{\frac{3}{2}}})
integral of (sin(1/x))/(x^2)	\int\:\frac{\sin(\frac{1}{x})}{x^{2}}dx
integral of x^4sqrt(4+x^5)	\int\:x^{4}\sqrt{4+x^{5}}dx
limit as x approaches 0+of x^2+3	\lim\:_{x\to\:0+}(x^{2}+3)
(\partial)/(\partial x)(9xsin(8x^2y))	\frac{\partial\:}{\partial\:x}(9x\sin(8x^{2}y))
laplacetransform e^{3t}cos(2t)	laplacetransform\:e^{3t}\cos(2t)
derivative of sin^2(e^{sin^2(x}))	\frac{d}{dx}(\sin^{2}(e^{\sin^{2}(x)}))
integral of 3xcos^3(x^2+2)	\int\:3x\cos^{3}(x^{2}+2)dx
tangent of f(x)=x^2,\at m(x)=-1/2	tangent\:f(x)=x^{2},\at\:m(x)=-\frac{1}{2}
derivative of sqrt(r^2-8x^2)	\frac{d}{dx}(\sqrt{r^{2}-8x^{2}})
integral of x(x+4)^{-3/2}	\int\:x(x+4)^{-\frac{3}{2}}dx
sum from n=1 to infinity of (-1)^nn^{-3}	\sum\:_{n=1}^{\infty\:}(-1)^{n}n^{-3}
integral of 1/(x^2sqrt(x^2-81))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-81}}dx
integral from-1 to 3 of (-x^3+3x^2+1)	\int\:_{-1}^{3}(-x^{3}+3x^{2}+1)dx
implicit (-8x)/y =0	implicit\:\frac{-8x}{y}=0
limit as x approaches 1 of x^3(5-x)	\lim\:_{x\to\:1}(x^{3}(5-x))
limit as x approaches 1 of x^{1/(1-x)}	\lim\:_{x\to\:1}(x^{\frac{1}{1-x}})
sum from n=1 to infinity of n(2/3)^n	\sum\:_{n=1}^{\infty\:}n(\frac{2}{3})^{n}
area y=sin(x),y=x,x= pi/2 ,x=pi	area\:y=\sin(x),y=x,x=\frac{π}{2},x=π
derivative of sqrt(3+5sin(x))	derivative\:\sqrt{3+5\sin(x)}
integral from 0 to a of 7xsqrt(a^2-x^2)	\int\:_{0}^{a}7x\sqrt{a^{2}-x^{2}}dx
roots (ax)/(x^2+a^2)	roots\:\frac{ax}{x^{2}+a^{2}}
(dy)/(dx)+2xy=-xy^4	\frac{dy}{dx}+2xy=-xy^{4}
derivative of x^2e^{-x^3}	\frac{d}{dx}(x^{2}e^{-x^{3}})

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