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Popular Calculus Problems

derivative of f(x)= 1/(x^2)	derivative\:f(x)=\frac{1}{x^{2}}
derivative of x^3-3x^2+4	\frac{d}{dx}(x^{3}-3x^{2}+4)
integral of 1/(csc(5x)sqrt(cos(5x)))	\int\:\frac{1}{\csc(5x)\sqrt{\cos(5x)}}dx
derivative of e^{2x+y}	\frac{d}{dx}(e^{2x+y})
integral of (-5x-41)/(x^2+x-12)	\int\:\frac{-5x-41}{x^{2}+x-12}dx
integral of (x^4-5e^{-2x})	\int\:(x^{4}-5e^{-2x})dx
derivative of (x^2+4x-5^3)	\frac{d}{dx}((x^{2}+4x-5)^{3})
(\partial)/(\partial x)(sqrt(x^2+2y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+2y^{2}})
x(dy)/(dx)+y=x,y(1)=3	x\frac{dy}{dx}+y=x,y(1)=3
d/(dt)(e^tsin(9t))	\frac{d}{dt}(e^{t}\sin(9t))
integral from 0 to (3pi)/2 of cos^3(37x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(37x)dx
integral of (cos(x))/(sqrt((1-sin(x))))	\int\:\frac{\cos(x)}{\sqrt{(1-\sin(x))}}dx
area 8x^2-x^3,x^2+11x,0,5	area\:8x^{2}-x^{3},x^{2}+11x,0,5
integral of 5xarcsin(5x)	\int\:5x\arcsin(5x)dx
integral of (4xy^2+3ysqrt(x))	\int\:(4xy^{2}+3y\sqrt{x})dx
integral of log_{3}(2x)	\int\:\log_{3}(2x)dx
integral of (x^4)/(12)	\int\:\frac{x^{4}}{12}dx
(d^9)/(dx^9)((2x+5)^7)	\frac{d^{9}}{dx^{9}}((2x+5)^{7})
y^{''}+y=xcos(x)	y^{\prime\:\prime\:}+y=x\cos(x)
integral of sin^2(4x)	\int\:\sin^{2}(4x)dx
d/(dy)(sqrt(10y-y^2))	\frac{d}{dy}(\sqrt{10y-y^{2}})
(\partial)/(\partial y)(x^{y-1})	\frac{\partial\:}{\partial\:y}(x^{y-1})
x((dy)/(dx))+2y=3	x(\frac{dy}{dx})+2y=3
(dy)/(dx)y=7^x	\frac{dy}{dx}y=7^{x}
(\partial)/(\partial y)(2/y)	\frac{\partial\:}{\partial\:y}(\frac{2}{y})
x^2y^'-4xy=sin(3x)x^6	x^{2}y^{\prime\:}-4xy=\sin(3x)x^{6}
derivative of f(x)=2sec(x)tan(x)	derivative\:f(x)=2\sec(x)\tan(x)
integral of ((6+e^x)^2)/(e^x)	\int\:\frac{(6+e^{x})^{2}}{e^{x}}dx
f(x)=e^{sqrt(x)}+ln(x+1)	f(x)=e^{\sqrt{x}}+\ln(x+1)
derivative of 1/(2x^{1/2)}+1/(4x^{3/4)}	derivative\:\frac{1}{2x^{\frac{1}{2}}}+\frac{1}{4x^{\frac{3}{4}}}
sum from k=1 to infinity of k^{-2.4}	\sum\:_{k=1}^{\infty\:}k^{-2.4}
simplify 6x^2+(768)/x	simplify\:6x^{2}+\frac{768}{x}
limit as x approaches+1 of (-1)/(x-1)	\lim\:_{x\to\:+1}(\frac{-1}{x-1})
derivative of (ln(x^3+1)/(2^{x^4)-6})	\frac{d}{dx}(\frac{\ln(x^{3}+1)}{2^{x^{4}}-6})
integral of (1-2x)e^{-x}	\int\:(1-2x)e^{-x}dx
integral of 1/(1-u)	\int\:\frac{1}{1-u}du
integral of e^{-1x}	\int\:e^{-1x}dx
derivative of 49y^6-84y^3+36	derivative\:49y^{6}-84y^{3}+36
integral of 3/(x(x^4+7))	\int\:\frac{3}{x(x^{4}+7)}dx
integral of e^{7x+8}	\int\:e^{7x+8}dx
integral of (e^xsin(y)-y)	\int\:(e^{x}\sin(y)-y)dx
derivative of ln(tan^2(x))	derivative\:\ln(\tan^{2}(x))
area y=x,y=x^2-2,y=0	area\:y=x,y=x^{2}-2,y=0
xy^'-2y=x^4	xy^{\prime\:}-2y=x^{4}
sum from n=0 to infinity of e^{(2n-1)}	\sum\:_{n=0}^{\infty\:}e^{(2n-1)}
integral of (2x+1)/(x^2-x+3)	\int\:\frac{2x+1}{x^{2}-x+3}dx
limit as x approaches 2 of 8/x	\lim\:_{x\to\:2}(\frac{8}{x})
integral from 9 to infinity of 2/(x^3)	\int\:_{9}^{\infty\:}\frac{2}{x^{3}}dx
(ye^{xy}-1/y)dx(xe^{xy}-x/(y^2))dy=0	(ye^{xy}-\frac{1}{y})dx(xe^{xy}-\frac{x}{y^{2}})dy=0
derivative of f(x)=(5t+300)/(t^2+25)	derivative\:f(x)=\frac{5t+300}{t^{2}+25}
derivative of 2x^3+4x	derivative\:2x^{3}+4x
integral of x^2y^2	\int\:x^{2}y^{2}dx
derivative of (-7x^2+7)^5(-7x^2+4)^{-4}	derivative\:(-7x^{2}+7)^{5}(-7x^{2}+4)^{-4}
integral of (\sqrt[5]{x^2})	\int\:(\sqrt[5]{x^{2}})dx
taylor ln(1+4x)	taylor\:\ln(1+4x)
integral from 1 to 2 of (x^4)/8+1/(4x^2)	\int\:_{1}^{2}\frac{x^{4}}{8}+\frac{1}{4x^{2}}dx
integral of (-x^2cos(y)sin(y)-xcos(y))	\int\:(-x^{2}\cos(y)\sin(y)-x\cos(y))dy
(((x+1))/((x+1)^2+4))^'	(\frac{(x+1)}{(x+1)^{2}+4})^{\prime\:}
derivative of x^5sin(3x)	\frac{d}{dx}(x^{5}\sin(3x))
derivative of (x^5-6/x ^{-2})	\frac{d}{dx}((x^{5}-\frac{6}{x})^{-2})
integral from 0 to 1 of xe^x	\int\:_{0}^{1}xe^{x}dx
xyy^'=(y^2-1)^{3/2}	xyy^{\prime\:}=(y^{2}-1)^{\frac{3}{2}}
(\partial)/(\partial y)(xyz+xy^5+yz^5+zx^5)	\frac{\partial\:}{\partial\:y}(xyz+xy^{5}+yz^{5}+zx^{5})
integral from 0 to 1 of cos^2(2pix)	\int\:_{0}^{1}\cos^{2}(2πx)dx
derivative of x^{0.5}+2x^{-0.5}	\frac{d}{dx}(x^{0.5}+2x^{-0.5})
slope of (2.6)(-3.5)	slope\:(2.6)(-3.5)
derivative of 4sin(3x)	derivative\:4\sin(3x)
integral of (2-x)/(4x^2+4x-3)	\int\:\frac{2-x}{4x^{2}+4x-3}dx
(dy)/(dx)+x^2(3y-2)=0	\frac{dy}{dx}+x^{2}(3y-2)=0
integral of x^6	\int\:x^{6}dx
derivative of sqrt(((1-x)/(1+x)))	\frac{d}{dx}(\sqrt{\frac{(1-x)}{1+x}})
derivative of sqrt(9-6x)	\frac{d}{dx}(\sqrt{9-6x})
integral of (-4sin(2x)+3cos(3x))	\int\:(-4\sin(2x)+3\cos(3x))dx
derivative of x^2e^{19x}	derivative\:x^{2}e^{19x}
derivative of (2x^5+6)/(x^3)	derivative\:\frac{2x^{5}+6}{x^{3}}
area x^2,x+2,2,-1	area\:x^{2},x+2,2,-1
integral of-5x^5e^{x^6}	\int\:-5x^{5}e^{x^{6}}dx
integral of 9x	\int\:9xdx
28y^{''}-14y^'=0,y(-2)=3,y^'(3)=-1	28y^{\prime\:\prime\:}-14y^{\prime\:}=0,y(-2)=3,y^{\prime\:}(3)=-1
integral of 1/(e^x-9e^{-x)}	\int\:\frac{1}{e^{x}-9e^{-x}}dx
limit as x approaches infinity+of tan(x)	\lim\:_{x\to\:\infty\:+}(\tan(x))
limit as x approaches 0 of (arctan(x))/x	\lim\:_{x\to\:0}(\frac{\arctan(x)}{x})
derivative of (8x^2+8x+4/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+8x+4}{\sqrt{x}})
(\partial)/(\partial x)(sqrt(x+2y))	\frac{\partial\:}{\partial\:x}(\sqrt{x+2y})
integral of (5x+4)/((x+8)^2(x-1))	\int\:\frac{5x+4}{(x+8)^{2}(x-1)}dx
inverse oflaplace (s^2+9)/(s(s+4))	inverselaplace\:\frac{s^{2}+9}{s(s+4)}
(dy)/(dx)=(x-1)/(x+3)(y-2)/(y-3)	\frac{dy}{dx}=\frac{x-1}{x+3}\frac{y-2}{y-3}
inverse oflaplace (2s+3)/(s^2+6s+13)	inverselaplace\:\frac{2s+3}{s^{2}+6s+13}
derivative of x/(x-2)	derivative\:\frac{x}{x-2}
derivative of (2x/3+(x+1)^{2/3})	\frac{d}{dx}(\frac{2x}{3}+(x+1)^{\frac{2}{3}})
1/5 (dy)/(dx)=(1/5)^2-1/5	\frac{1}{5}\frac{dy}{dx}=(\frac{1}{5})^{2}-\frac{1}{5}
derivative of y+xcos(y)	\frac{d}{dx}(y+x\cos(y))
inverse oflaplace (5x+5)/(x^2-4)	inverselaplace\:\frac{5x+5}{x^{2}-4}
integral of (e^{ln(x)})/(x^2)	\int\:\frac{e^{\ln(x)}}{x^{2}}dx
derivative of (x^2-5x/(x+1))	\frac{d}{dx}(\frac{x^{2}-5x}{x+1})
limit as x approaches 4 of xsqrt(20-x^2)	\lim\:_{x\to\:4}(x\sqrt{20-x^{2}})
(\partial)/(\partial x)(12xy^2)	\frac{\partial\:}{\partial\:x}(12xy^{2})
integral from 0 to 1 of ((x^2+1)e^{-x})	\int\:_{0}^{1}((x^{2}+1)e^{-x})dx
f(x)=cos(pi/x)	f(x)=\cos(\frac{π}{x})
derivative of (x^2-1(-3x^3+2x))	\frac{d}{dx}((x^{2}-1)(-3x^{3}+2x))

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