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Popular Calculus Problems

integral of 2x(x^2+1)^9	\int\:2x(x^{2}+1)^{9}dx
derivative of-(x+1sin((x^2)/2))	\frac{d}{dx}(-(x+1)\sin(\frac{x^{2}}{2}))
slope of y=6sin(pix-y),(1,0)	slope\:y=6\sin(πx-y),(1,0)
integral of 2cos(2x)-1	\int\:2\cos(2x)-1dx
laplacetransform cos^2(2t)	laplacetransform\:\cos^{2}(2t)
inverse oflaplace (((s+1)^2+1))/s	inverselaplace\:\frac{((s+1)^{2}+1)}{s}
integral of 2x(x^2+3)^7	\int\:2x(x^{2}+3)^{7}dx
maclaurin x-e^{3x}	maclaurin\:x-e^{3x}
derivative of (\sqrt[3]{t})/(t-9)	derivative\:\frac{\sqrt[3]{t}}{t-9}
integral of 3/(8+6x)	\int\:\frac{3}{8+6x}dx
area y= 1/x ,y= 1/4 x	area\:y=\frac{1}{x},y=\frac{1}{4}x
limit as x approaches 1 of (x+2)/(x^3+8)	\lim\:_{x\to\:1}(\frac{x+2}{x^{3}+8})
integral of 2/(xln^3(x))	\int\:\frac{2}{x\ln^{3}(x)}dx
(\partial)/(\partial x)(x^4ln(yz))	\frac{\partial\:}{\partial\:x}(x^{4}\ln(yz))
sum from n=1 to infinity of 1/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{10^{n}}
sum from n=1 to infinity of (2/7)*n	\sum\:_{n=1}^{\infty\:}(\frac{2}{7})\cdot\:n
integral of sin^4(x/2)cos^2(x/2)	\int\:\sin^{4}(\frac{x}{2})\cos^{2}(\frac{x}{2})dx
integral of 2t+2	\int\:2t+2dt
sum from n=0 to infinity of (-14)/8	\sum\:_{n=0}^{\infty\:}\frac{-14}{8}
derivative of \sqrt[5]{ln(x})	\frac{d}{dx}(\sqrt[5]{\ln(x)})
derivative of 3sin(x+2cos(x)tan(x))	\frac{d}{dx}(3\sin(x)+2\cos(x)\tan(x))
area 2x+1,x^3-5x^2+6x+1	area\:2x+1,x^{3}-5x^{2}+6x+1
integral of-30x^{2/3}	\int\:-30x^{\frac{2}{3}}dx
(dy)/(dx)=((e^{x-y}))/(1+e^x)	\frac{dy}{dx}=\frac{(e^{x-y})}{1+e^{x}}
integral from 0 to 2 of 30000e^{0.03x}	\int\:_{0}^{2}30000e^{0.03x}dx
integral of 36t^8e^{-t^9}	\int\:36t^{8}e^{-t^{9}}dt
limit as x approaches-1 of sqrt(5-11x)	\lim\:_{x\to\:-1}(\sqrt{5-11x})
(\partial)/(\partial x)(x/(y^2)+xy+2)	\frac{\partial\:}{\partial\:x}(\frac{x}{y^{2}}+xy+2)
tangent of x^2+5	tangent\:x^{2}+5
derivative of (x^3/3+7x^2+50x)	\frac{d}{dx}(\frac{x^{3}}{3}+7x^{2}+50x)
(\partial)/(\partial x)(5arccot(x))	\frac{\partial\:}{\partial\:x}(5\arccot(x))
derivative of (2x-8^4(x^2+x+1)^5)	\frac{d}{dx}((2x-8)^{4}(x^{2}+x+1)^{5})
integral of (e^{x-y})/(1+e^x)	\int\:\frac{e^{x-y}}{1+e^{x}}
derivative of log_{3}(3x-7)	\frac{d}{dx}(\log_{3}(3x-7))
integral of 8xe^{15x}	\int\:8xe^{15x}dx
derivative of (-x^2+y^2/((x^2+y^2)^2))	\frac{d}{dx}(\frac{-x^{2}+y^{2}}{(x^{2}+y^{2})^{2}})
(dy)/(dt)=-y/t+2	\frac{dy}{dt}=-\frac{y}{t}+2
implicit (dy)/(dx),xy+x=2	implicit\:\frac{dy}{dx},xy+x=2
integral of (sqrt(a^2+x^2))/(x^2)	\int\:\frac{\sqrt{a^{2}+x^{2}}}{x^{2}}dx
area y=6x-x^2,y=x	area\:y=6x-x^{2},y=x
integral from 5 to 8 of 5/(sqrt(x-5))	\int\:_{5}^{8}\frac{5}{\sqrt{x-5}}dx
(\partial)/(\partial x)(u/(1+2.4(x/y)))	\frac{\partial\:}{\partial\:x}(\frac{u}{1+2.4(\frac{x}{y})})
(\partial)/(\partial x)(6x^5y^6+5x^4y^7)	\frac{\partial\:}{\partial\:x}(6x^{5}y^{6}+5x^{4}y^{7})
integral from 0 to 3 of 15x	\int\:_{0}^{3}15xdx
limit as x approaches 0 of x(x)	\lim\:_{x\to\:0}(x(x))
limit as x approaches-2 of (x^2-6)/(2-x)	\lim\:_{x\to\:-2}(\frac{x^{2}-6}{2-x})
inverse oflaplace 1/(s^3+s^2)	inverselaplace\:\frac{1}{s^{3}+s^{2}}
derivative of 3^{1-2n}	derivative\:3^{1-2n}
(\partial)/(\partial x)(3xy-x^2y^2+23)	\frac{\partial\:}{\partial\:x}(3xy-x^{2}y^{2}+23)
(dy)/(dx)=(sqrt(x))/(e^y)	\frac{dy}{dx}=\frac{\sqrt{x}}{e^{y}}
derivative of sqrt(3x^2-2)	derivative\:\sqrt{3x^{2}-2}
derivative of f(x)=-9.8x^2+2x+1	derivative\:f(x)=-9.8x^{2}+2x+1
integral of 1/(arcsin(x)sqrt(1-x^2))	\int\:\frac{1}{\arcsin(x)\sqrt{1-x^{2}}}dx
(\partial)/(\partial x)(x^2+xy+y^2+2x-y)	\frac{\partial\:}{\partial\:x}(x^{2}+xy+y^{2}+2x-y)
d/(dt)(-cos(2t))	\frac{d}{dt}(-\cos(2t))
tangent of y=x^8e^{-x},(1, 1/e)	tangent\:y=x^{8}e^{-x},(1,\frac{1}{e})
integral of (2x^4-8x^3)*e^{-3x}	\int\:(2x^{4}-8x^{3})\cdot\:e^{-3x}dx
derivative of (2cos(x)/(sec(x)))	\frac{d}{dx}(\frac{2\cos(x)}{\sec(x)})
y^{''}+y^'+6y=0,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y^{\prime\:}+6y=0,y(0)=0,y^{\prime\:}(0)=0
(2xy)dy+(x^2+y^2)dx=0	(2xy)dy+(x^{2}+y^{2})dx=0
y^{''}-6y^'+25y=0,y(0)=3,y^'(0)=1	y^{\prime\:\prime\:}-6y^{\prime\:}+25y=0,y(0)=3,y^{\prime\:}(0)=1
derivative of y=(tan(x))^{9/x}	derivative\:y=(\tan(x))^{\frac{9}{x}}
integral of (x^2sqrt(x))	\int\:(x^{2}\sqrt{x})dx
derivative of 6x^{1/4}	derivative\:6x^{\frac{1}{4}}
integral of (3x)/((1-x^2)^3)	\int\:\frac{3x}{(1-x^{2})^{3}}dx
e^ydx+xe^ydy=0	e^{y}dx+xe^{y}dy=0
(\partial)/(\partial x)(cos^2(x))	\frac{\partial\:}{\partial\:x}(\cos^{2}(x))
derivative of (x^2(x^2+9x))^6	derivative\:(x^{2}(x^{2}+9x))^{6}
(\partial)/(\partial x)(ln(x+y^2))	\frac{\partial\:}{\partial\:x}(\ln(x+y^{2}))
(\partial)/(\partial x)((2xy)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{2xy}{x+y})
integral of wsqrt(w^2-ln(3))	\int\:w\sqrt{w^{2}-\ln(3)}dw
limit as x approaches 0 of (3x)/(xe^x)	\lim\:_{x\to\:0}(\frac{3x}{xe^{x}})
integral of (3x^2-2x+5)/(x^2)	\int\:\frac{3x^{2}-2x+5}{x^{2}}dx
x^3(dy)/(dx)+y^2=x^2y	x^{3}\frac{dy}{dx}+y^{2}=x^{2}y
longdivision (3x^2+1)/(2x^2-5)	longdivision\:\frac{3x^{2}+1}{2x^{2}-5}
derivative of f(x)=x^3sqrt(x)	derivative\:f(x)=x^{3}\sqrt{x}
limit as x approaches-3+of sqrt(x^3+27)	\lim\:_{x\to\:-3+}(\sqrt{x^{3}+27})
integral from 0 to 8 of e^xsin(x)	\int\:_{0}^{8}e^{x}\sin(x)dx
(\partial)/(\partial u)(u^2+v)	\frac{\partial\:}{\partial\:u}(u^{2}+v)
limit as x approaches 0+of x^{x^5}	\lim\:_{x\to\:0+}(x^{x^{5}})
derivative of (ln(6x))/(6x)	derivative\:\frac{\ln(6x)}{6x}
integral of ((3+ln(x))^3+12)/(4x)	\int\:\frac{(3+\ln(x))^{3}+12}{4x}dx
derivative of 2cos(x+sin(2x))	\frac{d}{dx}(2\cos(x)+\sin(2x))
derivative of ax+b/x	\frac{d}{dx}(ax+\frac{b}{x})
derivative of (e^x/(x^2-1))	\frac{d}{dx}(\frac{e^{x}}{x^{2}-1})
laplacetransform e^{-7t}	laplacetransform\:e^{-7t}
integral of x*sin(x)cos(x)	\int\:x\cdot\:\sin(x)\cos(x)dx
sum from n=7 to infinity of 1/(nln(n))	\sum\:_{n=7}^{\infty\:}\frac{1}{n\ln(n)}
integral from 0 to 3 of \|x^2-9\|	\int\:_{0}^{3}\left\|x^{2}-9\right\|dx
integral of-e^{-2x}	\int\:-e^{-2x}dx
derivative of (64)/(x^2+16)	derivative\:\frac{64}{x^{2}+16}
tangent of f(x)=x^2-4x,\at x=1	tangent\:f(x)=x^{2}-4x,\at\:x=1
derivative of-5sin(x)	\frac{d}{dx}(-5\sin(x))
(\partial)/(\partial x)(sqrt(2-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{2-x^{2}-y^{2}})
derivative of-e^{-4x}	\frac{d}{dx}(-e^{-4x})
integral from 3 to infinity of (e^{-1/x})/(x^2)	\int\:_{3}^{\infty\:}\frac{e^{-\frac{1}{x}}}{x^{2}}dx
(cos(x))^'	(\cos(x))^{\prime\:}
(\partial)/(\partial x)(y/(1+x))	\frac{\partial\:}{\partial\:x}(\frac{y}{1+x})
integral of (sqrt(x)+1)	\int\:(\sqrt{x}+1)dx
integral of (2^x+4e^x+x^3+5)	\int\:(2^{x}+4e^{x}+x^{3}+5)dx

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