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Popular Calculus Problems

derivative of y= 4/x+sqrt(x+0.5)-5x	derivative\:y=\frac{4}{x}+\sqrt{x+0.5}-5x
limit as t approaches 0 of (sin^2(3t))/t	\lim\:_{t\to\:0}(\frac{\sin^{2}(3t)}{t})
(\partial)/(\partial y)(1/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{2}+y^{2}+z^{2}})
sum from n=1 to infinity of 5/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{5}{10^{n}}
derivative of y=14sqrt(x)	derivative\:y=14\sqrt{x}
integral from 1 to 5 of (x^2+2)/(6x-x^2)	\int\:_{1}^{5}\frac{x^{2}+2}{6x-x^{2}}dx
area y^2-2x=2,x-y=3	area\:y^{2}-2x=2,x-y=3
integral of 2/(x-1)	\int\:\frac{2}{x-1}dx
limit as x approaches 3pi+of csc(x)	\lim\:_{x\to\:3π+}(\csc(x))
f(x)=-5/(x^2)	f(x)=-\frac{5}{x^{2}}
y^{''}+2y^'+37y=5e^{-t}cos(6t)	y^{\prime\:\prime\:}+2y^{\prime\:}+37y=5e^{-t}\cos(6t)
integral of e^{ax}sin(0x)	\int\:e^{ax}\sin(0x)dx
f(x)=8x-3	f(x)=8x-3
integral of sec^6(7x)	\int\:\sec^{6}(7x)dx
implicit (dy)/(dx),y^{2/3}-x^2+xy=1	implicit\:\frac{dy}{dx},y^{\frac{2}{3}}-x^{2}+xy=1
(\partial)/(\partial x)(5xsin(3x^2y))	\frac{\partial\:}{\partial\:x}(5x\sin(3x^{2}y))
tangent of f(x)=sqrt(x^2-x+13),\at x=4	tangent\:f(x)=\sqrt{x^{2}-x+13},\at\:x=4
integral of (x^2)/(x^3)+5	\int\:\frac{x^{2}}{x^{3}}+5dx
derivative of r/(sqrt(r^2+3))	derivative\:\frac{r}{\sqrt{r^{2}+3}}
laplacetransform 8sin(t)	laplacetransform\:8\sin(t)
sum from k=1 to infinity of (k^3)/(5^k)	\sum\:_{k=1}^{\infty\:}\frac{k^{3}}{5^{k}}
integral of (7sin(x)+2sec(x))/(tan(x))	\int\:\frac{7\sin(x)+2\sec(x)}{\tan(x)}dx
inverse oflaplace s/(2s+4)	inverselaplace\:\frac{s}{2s+4}
(\partial)/(\partial x)(5/(xy)+x/y+y/x)	\frac{\partial\:}{\partial\:x}(\frac{5}{xy}+\frac{x}{y}+\frac{y}{x})
derivative of x^3+x^2-5x	\frac{d}{dx}(x^{3}+x^{2}-5x)
integral of x*e^{5x}	\int\:x\cdot\:e^{5x}dx
integral of (x-1)^2(x-2)(x-4)	\int\:(x-1)^{2}(x-2)(x-4)dx
(\partial)/(\partial x)((7x)/(4+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{7x}{4+x^{2}+y^{2}})
(log_{10}(1+x))^'	(\log_{10}(1+x))^{\prime\:}
laplacetransform-8x	laplacetransform\:-8x
integral of arctan(x/4)	\int\:\arctan(\frac{x}{4})dx
integral of ((x^2+2x+1)/(x^2))	\int\:(\frac{x^{2}+2x+1}{x^{2}})dx
integral of 3sin^2(t)	\int\:3\sin^{2}(t)dt
y^{'''}+6y^{''}+11y^'+6y=0	y^{\prime\:\prime\:\prime\:}+6y^{\prime\:\prime\:}+11y^{\prime\:}+6y=0
(9y^2-xy)dx+(x^2)dy=0	(9y^{2}-xy)dx+(x^{2})dy=0
integral of (x^3)/(x^2+9)	\int\:\frac{x^{3}}{x^{2}+9}dx
derivative of 4^{-3}(2/(s^7)+3s)^4	derivative\:4^{-3}(\frac{2}{s^{7}}+3s)^{4}
integral of (2x+3)/(x^2+1)	\int\:\frac{2x+3}{x^{2}+1}dx
implicit (dy)/(dx),1=(y/x)	implicit\:\frac{dy}{dx},1=(\frac{y}{x})
derivative of f(x)=8cos(t)	derivative\:f(x)=8\cos(t)
integral of (ln(x^{18}))/x	\int\:\frac{\ln(x^{18})}{x}dx
derivative of 10cos(x)	derivative\:10\cos(x)
integral of 1/(x(x^2-8))	\int\:\frac{1}{x(x^{2}-8)}dx
integral of (2e^{2x})/(e^{2x)+12e^x+35}	\int\:\frac{2e^{2x}}{e^{2x}+12e^{x}+35}dx
derivative of y=((2x^2-1)^3)/((5x-8)^2)	derivative\:y=\frac{(2x^{2}-1)^{3}}{(5x-8)^{2}}
(dy)/(dx)=2y	\frac{dy}{dx}=2y
limit as x approaches 0-of cos(x)	\lim\:_{x\to\:0-}(\cos(x))
(\partial)/(\partial x)(2y-x)	\frac{\partial\:}{\partial\:x}(2y-x)
derivative of cos((1-e^{8x})/(1+e^{8x)})	derivative\:\cos(\frac{1-e^{8x}}{1+e^{8x}})
limit as x approaches 7 of 4/((x-7)^2)	\lim\:_{x\to\:7}(\frac{4}{(x-7)^{2}})
taylor 2xe^{-4x}	taylor\:2xe^{-4x}
integral of 1-1/(x^2)	\int\:1-\frac{1}{x^{2}}dx
integral of 7x^2e^{6x}	\int\:7x^{2}e^{6x}dx
tangent of f(x)=(x+2sin(x))	tangent\:f(x)=(x+2\sin(x))
integral of (x-3)/(sqrt(3-4x^2))	\int\:\frac{x-3}{\sqrt{3-4x^{2}}}dx
(dy)/(dx)=8xy	\frac{dy}{dx}=8xy
integral of x^2-7	\int\:x^{2}-7dx
y^{''}-2y^'+y=(e^t)/((1+t^2))	y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{e^{t}}{(1+t^{2})}
integral of 1/x e^{-x}	\int\:\frac{1}{x}e^{-x}dx
derivative of sqrt(3x+\sqrt{x)}	\frac{d}{dx}(\sqrt{3x+\sqrt{x}})
derivative of 2x(x+4^3)	\frac{d}{dx}(2x(x+4)^{3})
integral of e^{-t}cos(t)	\int\:e^{-t}\cos(t)dt
d/(dt)(1/2 e^{-4t}cos(8t))	\frac{d}{dt}(\frac{1}{2}e^{-4t}\cos(8t))
integral of x^3sin(5x)	\int\:x^{3}\sin(5x)dx
integral of x*sin(x/2)	\int\:x\cdot\:\sin(\frac{x}{2})dx
tangent of 0.72x^3-4.8x^2+0.6x+7.6	tangent\:0.72x^{3}-4.8x^{2}+0.6x+7.6
derivative of f(x)=2sin^4(sqrt(x))	derivative\:f(x)=2\sin^{4}(\sqrt{x})
integral of x^2+e^x	\int\:x^{2}+e^{x}dx
tangent of y=(sqrt(x))/(8x-4),\at x=2	tangent\:y=\frac{\sqrt{x}}{8x-4},\at\:x=2
limit as s approaches 1 of (s^3-1)/(s-1)	\lim\:_{s\to\:1}(\frac{s^{3}-1}{s-1})
integral from-infinity to 0 of (xe^{2x})	\int\:_{-\infty\:}^{0}(xe^{2x})dx
derivative of cos^4(3x^2)	\frac{d}{dx}(\cos^{4}(3x^{2}))
integral from-1 to-2 of (16-x^3)/(x^3)	\int\:_{-1}^{-2}\frac{16-x^{3}}{x^{3}}dx
integral of 5sin^3(5x)cos^3(5x)	\int\:5\sin^{3}(5x)\cos^{3}(5x)dx
(\partial)/(\partial x)(x^2y+e^{xy})	\frac{\partial\:}{\partial\:x}(x^{2}y+e^{xy})
integral from 0 to 4.5 of 90x	\int\:_{0}^{4.5}90xdx
derivative of 1+2tan(x)	\frac{d}{dx}(1+2\tan(x))
limit as x approaches 0 of x^2-1	\lim\:_{x\to\:0}(x^{2}-1)
integral of ln(x)sqrt(x^{15)}	\int\:\ln(x)\sqrt{x^{15}}dx
tangent of 3/((4x+1)^2)	tangent\:\frac{3}{(4x+1)^{2}}
derivative of (x^3/3+1)	\frac{d}{dx}(\frac{x^{3}}{3}+1)
derivative of 2x-x^2+2x^3	\frac{d}{dx}(2x-x^{2}+2x^{3})
integral of csc^3(5x)	\int\:\csc^{3}(5x)dx
integral of 1/((x^2-2x+5)^2)	\int\:\frac{1}{(x^{2}-2x+5)^{2}}dx
f(x)=-x^4+18x^2-11	f(x)=-x^{4}+18x^{2}-11
derivative of (x^2+7\sqrt[3]{x^2+2})	\frac{d}{dx}((x^{2}+7)\sqrt[3]{x^{2}+2})
integral of-4sin(4t)+1	\int\:-4\sin(4t)+1dt
limit as x approaches+4 of 9x+\|x-4\|	\lim\:_{x\to\:+4}(9x+\left\|x-4\right\|)
derivative of-sin^3(x)	derivative\:-\sin^{3}(x)
(\partial)/(\partial x)(2ysin(x)-x^3+ln(y))	\frac{\partial\:}{\partial\:x}(2y\sin(x)-x^{3}+\ln(y))
integral of ((x-1))/(x^2+x+1)	\int\:\frac{(x-1)}{x^{2}+x+1}dx
integral from 0 to 1 of x(sqrt(x)-x)	\int\:_{0}^{1}x(\sqrt{x}-x)dx
derivative of ln(sqrt(x-2))	\frac{d}{dx}(\ln(\sqrt{x-2}))
integral from 0 to pi of (5e^x+5sin(x))	\int\:_{0}^{π}(5e^{x}+5\sin(x))dx
derivative of f(x)= 1/(2x)	derivative\:f(x)=\frac{1}{2x}
(\partial)/(\partial x)(sin(xy^2))	\frac{\partial\:}{\partial\:x}(\sin(xy^{2}))
derivative of (x^2-2)/(e^{2x)}	derivative\:\frac{x^{2}-2}{e^{2x}}
limit as x approaches-1 of log_{10}(x)	\lim\:_{x\to\:-1}(\log_{10}(x))
integral of (8x^2+3x^{-2})	\int\:(8x^{2}+3x^{-2})dx
integral of (10)/(cos(x)-1)	\int\:\frac{10}{\cos(x)-1}dx

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