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Popular Calculus Problems

derivative of e^{8e^x}	derivative\:e^{8e^{x}}
integral from 5 to infinity of xe^{-3x}	\int\:_{5}^{\infty\:}xe^{-3x}dx
integral from 0 to 8 of sqrt(x+1)	\int\:_{0}^{8}\sqrt{x+1}dx
(dx)/(dt)+0.1x=10	\frac{dx}{dt}+0.1x=10
integral of (6s^2-2)/(s^3)	\int\:\frac{6s^{2}-2}{s^{3}}ds
derivative of 2x^2-3x+5	derivative\:2x^{2}-3x+5
integral of sqrt(16x^5)	\int\:\sqrt{16x^{5}}dx
integral of (8x(x^7-1/8))	\int\:(8x(x^{7}-\frac{1}{8}))dx
integral of ((x^2+x+1))/((2x+1)(x^2+1))	\int\:\frac{(x^{2}+x+1)}{(2x+1)(x^{2}+1)}dx
integral of 7x-3	\int\:7x-3dx
integral of (sin(x)sqrt(1+cos(x)))	\int\:(\sin(x)\sqrt{1+\cos(x)})dx
derivative of ln(sec^3(x^4-1))	\frac{d}{dx}(\ln(\sec^{3}(x^{4}-1)))
sum from n=0 to infinity of cos^2(n)	\sum\:_{n=0}^{\infty\:}\cos^{2}(n)
(\partial)/(\partial x)(2x^{1/2})	\frac{\partial\:}{\partial\:x}(2x^{\frac{1}{2}})
d/(dy)(4y^3)	\frac{d}{dy}(4y^{3})
integral from 0 to 9 of (2x^3+1)	\int\:_{0}^{9}(2x^{3}+1)dx
derivative of 3x^2-1	\frac{d}{dx}(3x^{2}-1)
integral of (x^2+1)^{-1}	\int\:(x^{2}+1)^{-1}dx
derivative of f(x)=4^x-x^2+3ln(x)	derivative\:f(x)=4^{x}-x^{2}+3\ln(x)
integral from-2 to 2 of 1/(x^2)	\int\:_{-2}^{2}\frac{1}{x^{2}}dx
integral of 2e^x+2x-1	\int\:2e^{x}+2x-1dx
(x^2y^3-1/(1+9x^2))dx+x^3y^2dy=0	(x^{2}y^{3}-\frac{1}{1+9x^{2}})dx+x^{3}y^{2}dy=0
(\partial)/(\partial y)(ln(x^4+y)-z)	\frac{\partial\:}{\partial\:y}(\ln(x^{4}+y)-z)
d/(dy)(ln(x-2y))	\frac{d}{dy}(\ln(x-2y))
d/(d{r)}(pi{r}^2)	\frac{d}{d{r}}(π{r}^{2})
derivative of ln(ln(9x))	\frac{d}{dx}(\ln(\ln(9x)))
integral from 0 to 9 of 2piy(3-y/3)	\int\:_{0}^{9}2πy(3-\frac{y}{3})dy
derivative of-(5e^{5/x}/(x^2))	\frac{d}{dx}(-\frac{5e^{\frac{5}{x}}}{x^{2}})
(\partial)/(\partial x)(30-(x^2+y^2))	\frac{\partial\:}{\partial\:x}(30-(x^{2}+y^{2}))
integral of sin^5(11x)	\int\:\sin^{5}(11x)dx
integral of ([sin(x)]^2x+[cos(x)]^2x)	\int\:([\sin(x)]^{2}x+[\cos(x)]^{2}x)dx
integral of ((1+x)^3)/(sqrt(x))	\int\:\frac{(1+x)^{3}}{\sqrt{x}}dx
integral from 1 to infinity of 1/(4+x^2)	\int\:_{1}^{\infty\:}\frac{1}{4+x^{2}}dx
integral from-1 to 0 of-5x(3x^2-2)^3	\int\:_{-1}^{0}-5x(3x^{2}-2)^{3}dx
(dP)/(dt)=P(10^{-1}-10^{-7}P),P(0)=7000	\frac{dP}{dt}=P(10^{-1}-10^{-7}P),P(0)=7000
integral of (sqrt(25-x^2))	\int\:(\sqrt{25-x^{2}})dx
derivative of xsqrt(1-x)	\frac{d}{dx}(x\sqrt{1-x})
integral of sqrt(7+x^2)	\int\:\sqrt{7+x^{2}}dx
x^{''}-0.1x^'+x=0	x^{\prime\:\prime\:}-0.1x^{\prime\:}+x=0
integral of (x/2)^2	\int\:(\frac{x}{2})^{2}dx
tangent of f(x)=x^4-8x^3+4,\at x=-1	tangent\:f(x)=x^{4}-8x^{3}+4,\at\:x=-1
(x^2+(2y)/x)dx=(3-ln(x^2))dy	(x^{2}+\frac{2y}{x})dx=(3-\ln(x^{2}))dy
derivative of (2x^5-5x^3+7x^4)	\frac{d}{dx}((2x^{5}-5x^{3}+7x)^{4})
integral from 1 to 4 of x^2+2x-5	\int\:_{1}^{4}x^{2}+2x-5dx
limit as x approaches infinity+of (log_{4}(x))/(log_{7)(x)}	\lim\:_{x\to\:\infty\:+}(\frac{\log_{4}(x)}{\log_{7}(x)})
derivative of (x^2/(x^3+4))	\frac{d}{dx}(\frac{x^{2}}{x^{3}+4})
(dy)/(dx)=y^3xe^{x^2}	\frac{dy}{dx}=y^{3}xe^{x^{2}}
y^{''}-8y=0	y^{\prime\:\prime\:}-8y=0
ax^{''}+bx=0	ax^{\prime\:\prime\:}+bx=0
derivative of e^{tanh(2x})	\frac{d}{dx}(e^{\tanh(2x)})
integral of 1-cos(6x)	\int\:1-\cos(6x)dx
slope ofintercept (0.5)(1.6)	slopeintercept\:(0.5)(1.6)
(dy)/(dx)x^3+y^3=6xy	\frac{dy}{dx}x^{3}+y^{3}=6xy
y^'=(x(x^2+1))/(4y^3),y(0)=-1/(sqrt(2))	y^{\prime\:}=\frac{x(x^{2}+1)}{4y^{3}},y(0)=-\frac{1}{\sqrt{2}}
(\partial)/(\partial x)((a^2x^2+b^2y^2)^4)	\frac{\partial\:}{\partial\:x}((a^{2}x^{2}+b^{2}y^{2})^{4})
derivative of f(x)=sqrt(x^2-2x+1)	derivative\:f(x)=\sqrt{x^{2}-2x+1}
derivative of (x^3/3+c)	\frac{d}{dx}(\frac{x^{3}}{3}+c)
limit as x approaches 5 of (x^3+8)/(x+2)	\lim\:_{x\to\:5}(\frac{x^{3}+8}{x+2})
x(x+1)(dy)/(dx)+xy=1,y(e)=1	x(x+1)\frac{dy}{dx}+xy=1,y(e)=1
((sqrt(x)+x)dy)/(dx)=sqrt(y)+y	\frac{(\sqrt{x}+x)dy}{dx}=\sqrt{y}+y
derivative of f(x)=x^2-4	derivative\:f(x)=x^{2}-4
integral of 1/(x^2(x+1)^2)	\int\:\frac{1}{x^{2}(x+1)^{2}}dx
tangent of 7x-4sqrt(x)	tangent\:7x-4\sqrt{x}
y^'-y^{5/3}=0	y^{\prime\:}-y^{\frac{5}{3}}=0
integral of x/(x-20)	\int\:\frac{x}{x-20}dx
maclaurin 1/(1+\frac{1){1+x}}	maclaurin\:\frac{1}{1+\frac{1}{1+x}}
limit as x approaches 0 of log_{2}(x)	\lim\:_{x\to\:0}(\log_{2}(x))
integral of (x+6y)	\int\:(x+6y)dy
inverse oflaplace s/(s^2+2s-3)	inverselaplace\:\frac{s}{s^{2}+2s-3}
integral of 11y	\int\:11ydy
f(x)=xcos(x)-sin(x)	f(x)=x\cos(x)-\sin(x)
derivative of ln(x^2sin(x))	\frac{d}{dx}(\ln(x^{2})\sin(x))
integral of ((y^2+1))/(y^2+4)	\int\:\frac{(y^{2}+1)}{y^{2}+4}dy
integral of (xsin(x))/((cos(x))^2)	\int\:\frac{x\sin(x)}{(\cos(x))^{2}}dx
derivative of x^2y^4	\frac{d}{dx}(x^{2}y^{4})
limit as x approaches 2 of x^2-5	\lim\:_{x\to\:2}(x^{2}-5)
limit as x approaches 0 of (1-e^{-x})/x	\lim\:_{x\to\:0}(\frac{1-e^{-x}}{x})
derivative of (x^2/(x^3))	\frac{d}{dx}(\frac{x^{2}}{x^{3}})
derivative of e^x(x^2+1)(x+4)	derivative\:e^{x}(x^{2}+1)(x+4)
area y=-x,y=-x^2+ex	area\:y=-x,y=-x^{2}+ex
parity (csc(3x))/(x^3)	parity\:\frac{\csc(3x)}{x^{3}}
integral of (e^{-x})/(x^3)	\int\:\frac{e^{-x}}{x^{3}}dx
integral of 9tan^3(2x)sec^5(2x)	\int\:9\tan^{3}(2x)\sec^{5}(2x)dx
integral from-5 to 5 of sqrt(1+x^2)	\int\:_{-5}^{5}\sqrt{1+x^{2}}dx
(e^y)^'	(e^{y})^{\prime\:}
integral of (1-x^2)/2	\int\:\frac{1-x^{2}}{2}dx
derivative of log_{2}(x-1-2)	\frac{d}{dx}(\log_{2}(x-1)-2)
derivative of y=x^2e^x-2xe^x+6e^x	derivative\:y=x^{2}e^{x}-2xe^{x}+6e^{x}
tangent of f(x)=16sqrt(x),\at x=16	tangent\:f(x)=16\sqrt{x},\at\:x=16
simplify (2x^{-2}+3)^{-3}	simplify\:(2x^{-2}+3)^{-3}
integral of 1/(10^5x-x^2)	\int\:\frac{1}{10^{5}x-x^{2}}dx
integral of 4x^{1/3}+2x^{-1/3}	\int\:4x^{\frac{1}{3}}+2x^{-\frac{1}{3}}dx
y^'=y(xy^6+3)	y^{\prime\:}=y(xy^{6}+3)
2x^{''}+40x=0	2x^{\prime\:\prime\:}+40x=0
derivative of (sqrt(x)-5)/(sqrt(x)+5)	derivative\:\frac{\sqrt{x}-5}{\sqrt{x}+5}
laplacetransform f(t)=(1+e^{2t})^2	laplacetransform\:f(t)=(1+e^{2t})^{2}
derivative of 4-6x	\frac{d}{dx}(4-6x)
derivative of sqrt(x)-9	\frac{d}{dx}(\sqrt{x}-9)
(dx)/(dt)+tx^3+x/t =0	\frac{dx}{dt}+tx^{3}+\frac{x}{t}=0
integral of 1/(3\sqrt[3]{x^5)}	\int\:\frac{1}{3\sqrt[3]{x^{5}}}dx

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