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Popular Calculus Problems

integral of x/(sqrt(4-3x^2))	\int\:\frac{x}{\sqrt{4-3x^{2}}}dx
limit as x approaches 0 of (x+97)/x	\lim\:_{x\to\:0}(\frac{x+97}{x})
xy^'-2y=2x^2+2x+2	xy^{\prime\:}-2y=2x^{2}+2x+2
tangent of g(x)=3e^{-2x},(0,3)	tangent\:g(x)=3e^{-2x},(0,3)
derivative of f(x)=((x^2-1))/(x^2+x+1)	derivative\:f(x)=\frac{(x^{2}-1)}{x^{2}+x+1}
derivative of 1/3 ln(x)	\frac{d}{dx}(\frac{1}{3}\ln(x))
7ln(y)y^'-x^9y=0	7\ln(y)y^{\prime\:}-x^{9}y=0
integral of sin(2x)*sec(x)	\int\:\sin(2x)\cdot\:\sec(x)dx
integral of (6x^3-12x^2+4)/(x^2-2x)	\int\:\frac{6x^{3}-12x^{2}+4}{x^{2}-2x}dx
limit as x approaches 2pi of (x-2pi)/(sin(x))	\lim\:_{x\to\:2π}(\frac{x-2π}{\sin(x)})
derivative of tan(bx)	\frac{d}{dx}(\tan(bx))
taylor xcos(5x)	taylor\:x\cos(5x)
(y+x+(y^2)/x)dx-xdy=0	(y+x+\frac{y^{2}}{x})dx-xdy=0
integral of 6sin(x)+5	\int\:6\sin(x)+5dx
integral of x2^{-x}	\int\:x2^{-x}dx
(dy)/(dx)=3x^{-4}	\frac{dy}{dx}=3x^{-4}
(dy)/(dx)=2y-3y^2	\frac{dy}{dx}=2y-3y^{2}
integral from 0 to 2 of cos(x^2)	\int\:_{0}^{2}\cos(x^{2})dx
derivative of f(x)=e	derivative\:f(x)=e
derivative of f(x)=(2x-3)/(4x+1)	derivative\:f(x)=\frac{2x-3}{4x+1}
derivative of tan(e^{3x}+e^{tan(3x)})	\frac{d}{dx}(\tan(e^{3x})+e^{\tan(3x)})
integral of 3/2 sqrt(x+1)	\int\:\frac{3}{2}\sqrt{x+1}dx
laplacetransform sin(6(t-(3pi)/6)+3pi)	laplacetransform\:\sin(6(t-\frac{3π}{6})+3π)
(dy)/(dx)=(e^{x-y})/(1+e^x)	\frac{dy}{dx}=\frac{e^{x-y}}{1+e^{x}}
integral of (x^2)/((x^2-1)^{3/2)}	\int\:\frac{x^{2}}{(x^{2}-1)^{\frac{3}{2}}}dx
tangent of f(x)=x^2-5x,\at x=-2	tangent\:f(x)=x^{2}-5x,\at\:x=-2
integral of 9xsin(x)cos(x)	\int\:9x\sin(x)\cos(x)dx
tangent of f(x)=\|x\|sqrt(5-x^2),(2,2)	tangent\:f(x)=\left\|x\right\|\sqrt{5-x^{2}},(2,2)
limit as x approaches 2 of 3x+4x	\lim\:_{x\to\:2}(3x+4x)
integral from 2 to 4 of 2/(xsqrt(x^2-4))	\int\:_{2}^{4}\frac{2}{x\sqrt{x^{2}-4}}dx
limit as x approaches-1+of 2/(x+1)	\lim\:_{x\to\:-1+}(\frac{2}{x+1})
tangent of f(x)=5cos(x),\at x= pi/6	tangent\:f(x)=5\cos(x),\at\:x=\frac{π}{6}
limit as x approaches+10 of 8/((x-10)^2)	\lim\:_{x\to\:+10}(\frac{8}{(x-10)^{2}})
f(x)=4x^3-2/(x^3)	f(x)=4x^{3}-\frac{2}{x^{3}}
(dy)/((y^2+0.6y))= 1/x dx	\frac{dy}{(y^{2}+0.6y)}=\frac{1}{x}dx
derivative of e^{-x}(x-1)	\frac{d}{dx}(e^{-x}(x-1))
taylor f(x)=3^3-3(3)^2+4(3)+5+x	taylor\:f(x)=3^{3}-3(3)^{2}+4(3)+5+x
derivative of x/(2x+1)	derivative\:\frac{x}{2x+1}
integral of (\sqrt[7]{x^3})	\int\:(\sqrt[7]{x^{3}})dx
derivative of f(r)= r/(sqrt(r^2+7))	derivative\:f(r)=\frac{r}{\sqrt{r^{2}+7}}
integral of tan^2(w/2)+sec^2(w/2)	\int\:\tan^{2}(\frac{w}{2})+\sec^{2}(\frac{w}{2})dw
derivative of sin(3xcos(x))	\frac{d}{dx}(\sin(3x)\cos(x))
integral of (9x^2-7)	\int\:(9x^{2}-7)dx
integral of (-2y-2)/(y^2+y)	\int\:\frac{-2y-2}{y^{2}+y}dy
limit as x approaches 0-of x/(\|x+1\|)	\lim\:_{x\to\:0-}(\frac{x}{\left\|x+1\right\|})
integral of (16x^2)/((x-12)(x+4)^2)	\int\:\frac{16x^{2}}{(x-12)(x+4)^{2}}dx
integral of (1/8)y_{1}e^{-(y_{1}+y_{2})/2}_{1}	\int\:(\frac{1}{8})y_{1}e^{-\frac{y_{1}+y_{2}}{2}}dy_{1}
y^'=4xy	y^{\prime\:}=4xy
integral from-2 to 1 of sqrt(1+25)	\int\:_{-2}^{1}\sqrt{1+25}dx
limit as x approaches 27 of (3-\sqrt[3]{x})/(27-x)	\lim\:_{x\to\:27}(\frac{3-\sqrt[3]{x}}{27-x})
tangent of f(x)=(9-6x)^2,(1,9)	tangent\:f(x)=(9-6x)^{2},(1,9)
inverse oflaplace 1/(s^2(1+7s))	inverselaplace\:\frac{1}{s^{2}(1+7s)}
derivative of x(1-x/(10))	\frac{d}{dx}(x(1-\frac{x}{10}))
derivative of 5xcos(x^2)	\frac{d}{dx}(5x\cos(x^{2}))
limit as x approaches+0 of 5/(x^2+x)-5/x	\lim\:_{x\to\:+0}(\frac{5}{x^{2}+x}-\frac{5}{x})
derivative of ln((x-1)/(x+1))	derivative\:\ln(\frac{x-1}{x+1})
limit as x approaches 3 of (sin(x))/x	\lim\:_{x\to\:3}(\frac{\sin(x)}{x})
integral of (72)/(1-cos(9x))	\int\:\frac{72}{1-\cos(9x)}dx
tangent of ((4+x))/((x-2)),\at x=8	tangent\:\frac{(4+x)}{(x-2)},\at\:x=8
tangent of 4/x	tangent\:\frac{4}{x}
integral from 0 to pi/2 of-5cos^5(x)	\int\:_{0}^{\frac{π}{2}}-5\cos^{5}(x)dx
derivative of sqrt(3-x^2)	\frac{d}{dx}(\sqrt{3-x^{2}})
sum from n=3 to infinity of 2/(n(n+3))	\sum\:_{n=3}^{\infty\:}\frac{2}{n(n+3)}
(dh)/(dt)=4-16t^2,\quad h(1)=0	\frac{dh}{dt}=4-16t^{2},\quad\:h(1)=0
limit as x approaches 1+of 8/(x^3-1)	\lim\:_{x\to\:1+}(\frac{8}{x^{3}-1})
tangent of f(x)=(x^3-9x)^{10},(-3,0)	tangent\:f(x)=(x^{3}-9x)^{10},(-3,0)
d/(d{x)}({x}^{{y}{z}})	\frac{d}{d{x}}({x}^{{y}{z}})
2cos^2(y)dx+tan(y)dy=0	2\cos^{2}(y)dx+\tan(y)dy=0
derivative of (sqrt(3)/(2sqrt(x)))	\frac{d}{dx}(\frac{\sqrt{3}}{2\sqrt{x}})
(\partial)/(\partial y)(3+xln(xy-7))	\frac{\partial\:}{\partial\:y}(3+x\ln(xy-7))
derivative of f(x)=sqrt(1+x^2)	derivative\:f(x)=\sqrt{1+x^{2}}
(\partial)/(\partial x)(5arctan(x))	\frac{\partial\:}{\partial\:x}(5\arctan(x))
limit as x approaches+(-2) of log_{2}(8)	\lim\:_{x\to\:+(-2)}(\log_{2}(8))
integral of e^{-x+1}	\int\:e^{-x+1}dx
integral from-1 to 2 of x-2\|x\|	\int\:_{-1}^{2}x-2\left\|x\right\|dx
(\partial)/(\partial x)(9+ln(xy-5))	\frac{\partial\:}{\partial\:x}(9+\ln(xy-5))
integral of (8x^2+3x-6)/((x^2-4)(x+2))	\int\:\frac{8x^{2}+3x-6}{(x^{2}-4)(x+2)}dx
tangent of 2/(sqrt(x))-3e^x+3e^4	tangent\:\frac{2}{\sqrt{x}}-3e^{x}+3e^{4}
derivative of 75(1-5/x)	derivative\:75(1-\frac{5}{x})
sum from n=1 to infinity of (2/5)^{n-1}	\sum\:_{n=1}^{\infty\:}(\frac{2}{5})^{n-1}
limit as t approaches infinity of t^4	\lim\:_{t\to\:\infty\:}(t^{4})
derivative of f(x)=x^6(6x^3+x)^5	derivative\:f(x)=x^{6}(6x^{3}+x)^{5}
tangent of f(x)=e^{3x}*ln(4x)	tangent\:f(x)=e^{3x}\cdot\:\ln(4x)
sum from n=1 to infinity of (7/8)^n	\sum\:_{n=1}^{\infty\:}(\frac{7}{8})^{n}
integral of 5cos(5x)	\int\:5\cos(5x)dx
(\partial)/(\partial x)(V(x))	\frac{\partial\:}{\partial\:x}(V(x))
integral of sqrt(pi^2-x^2)	\int\:\sqrt{π^{2}-x^{2}}dx
integral of (x^2+3)/(x^3+5x)	\int\:\frac{x^{2}+3}{x^{3}+5x}dx
d/(dt)(Ae^{-t})	\frac{d}{dt}(Ae^{-t})
integral of e^pi	\int\:e^{π}dx
derivative of-16e^{-x^4}x^3	\frac{d}{dx}(-16e^{-x^{4}}x^{3})
integral from 0 to 1 of integral from 0 to y^2 of xe^{x/(y^2)}	\int\:_{0}^{1}\int\:_{0}^{y^{2}}xe^{\frac{x}{y^{2}}}dxdy
limit as x approaches 4 of (x^2-3x-4)/(x-4)	\lim\:_{x\to\:4}(\frac{x^{2}-3x-4}{x-4})
derivative of (3x+5/(x^2+4))	\frac{d}{dx}(\frac{3x+5}{x^{2}+4})
limit as x approaches 8 of 4x	\lim\:_{x\to\:8}(4x)
sum from n=1 to infinity of 6(5/4)^n	\sum\:_{n=1}^{\infty\:}6(\frac{5}{4})^{n}
sum from n=0 to infinity of ((1^n))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(1^{n})}{n!}
(\partial)/(\partial x)(x^2e^x)	\frac{\partial\:}{\partial\:x}(x^{2}e^{x})
derivative of (1-xln(1-x))	\frac{d}{dx}((1-x)\ln(1-x))
integral of (3x^2)/8	\int\:\frac{3x^{2}}{8}dx

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