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Popular Calculus Problems

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}})
derivative of sqrt(2x-2)	\frac{d}{dx}(\sqrt{2x-2})
derivative of 3x^2-10x+7	\frac{d}{dx}(3x^{2}-10x+7)
integral from 0 to 1 of (1+sqrt(x))^8	\int\:_{0}^{1}(1+\sqrt{x})^{8}dx
(\partial)/(\partial x)(e^{3xyz-2})	\frac{\partial\:}{\partial\:x}(e^{3xyz-2})
derivative of (3x+1/(x^2+1))	\frac{d}{dx}(\frac{3x+1}{x^{2}+1})
limit as x approaches pi/2 of (sin(x))/x	\lim\:_{x\to\:\frac{π}{2}}(\frac{\sin(x)}{x})
area x=(y^2)/4 ,x= y/2+2	area\:x=\frac{y^{2}}{4},x=\frac{y}{2}+2
sum from n=0 to infinity of nsin(npi)	\sum\:_{n=0}^{\infty\:}n\sin(nπ)
integral of x/(x(x+4))	\int\:\frac{x}{x(x+4)}dx
(\partial)/(\partial x)(e^x*y)	\frac{\partial\:}{\partial\:x}(e^{x}\cdot\:y)
derivative of f(x)=sqrt(x)+7/(sqrt(x))	derivative\:f(x)=\sqrt{x}+\frac{7}{\sqrt{x}}
integral of x*ln(1+x)	\int\:x\cdot\:\ln(1+x)dx
area x^3-5x^2-x+5,1,5	area\:x^{3}-5x^{2}-x+5,1,5
integral of e^{-2x}sin(x/2)	\int\:e^{-2x}\sin(\frac{x}{2})dx
derivative of f(x)=arctan(2/x)	derivative\:f(x)=\arctan(\frac{2}{x})
integral of x*cos(kx)	\int\:x\cdot\:\cos(kx)dx
tangent of-10x^4+x^3	tangent\:-10x^{4}+x^{3}
derivative of y=x^{13/14}	derivative\:y=x^{\frac{13}{14}}
sum from n=1 to infinity of ln((n+1)^2)	\sum\:_{n=1}^{\infty\:}\ln((n+1)^{2})

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