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Popular Calculus Problems

integral from 0 to 2 of integral from 3y to 6 of 5e^{x^2}	\int\:_{0}^{2}\int\:_{3y}^{6}5e^{x^{2}}dxdy
integral of 3xcos(5x)	\int\:3x\cos(5x)dx
integral of (4x+6)/(x^2+1)	\int\:\frac{4x+6}{x^{2}+1}dx
maclaurin (4x^2)(e^{-4x})	maclaurin\:(4x^{2})(e^{-4x})
integral of (1/x-3/(x^2+1))	\int\:(\frac{1}{x}-\frac{3}{x^{2}+1})dx
integral of (x^2-9x+5)	\int\:(x^{2}-9x+5)dx
limit as x approaches+1 of x^2	\lim\:_{x\to\:+1}(x^{2})
slope of (-6x^2-4x+4)/((3x^2+2)^2)	slope\:\frac{-6x^{2}-4x+4}{(3x^{2}+2)^{2}}
integral of (sin(y))/(cos^2(y))	\int\:\frac{\sin(y)}{\cos^{2}(y)}dy
limit as x approaches 2 of 1/3	\lim\:_{x\to\:2}(\frac{1}{3})
taylor x^{9/6},7	taylor\:x^{\frac{9}{6}},7
limit as x approaches 0+of (4x+1)^{cot(x)}	\lim\:_{x\to\:0+}((4x+1)^{\cot(x)})
integral of-2e^{-3cos(3x)}sin(3x)	\int\:-2e^{-3\cos(3x)}\sin(3x)dx
(\partial)/(\partial x)(e^{p(x)}(p(x)+p(x)sqrt(p(x))))	\frac{\partial\:}{\partial\:x}(e^{p(x)}(p(x)+p(x)\sqrt{p(x)}))
integral of e^{ax+b}	\int\:e^{ax+b}dx
d/(dt)(7cos^3(t))	\frac{d}{dt}(7\cos^{3}(t))
integral of (4cos^2(x))	\int\:(4\cos^{2}(x))dx
derivative of e^{e^{-x}}	derivative\:e^{e^{-x}}
integral of cos(3pit)	\int\:\cos(3πt)dt
integral of 1-3/y	\int\:1-\frac{3}{y}dy
f(x)=-8sin(x)	f(x)=-8\sin(x)
derivative of (1/(y^2)-7/(y^4))(y+9y^3)	derivative\:(\frac{1}{y^{2}}-\frac{7}{y^{4}})(y+9y^{3})
limit as x approaches 3 of 2x-3	\lim\:_{x\to\:3}(2x-3)
2y^{''}+33y=0	2y^{\prime\:\prime\:}+33y=0
limit as x approaches 1 of \sqrt[3]{x}	\lim\:_{x\to\:1}(\sqrt[3]{x})
sum from k=1 to infinity of ((-1)^k)/k	\sum\:_{k=1}^{\infty\:}\frac{(-1)^{k}}{k}
derivative of (6x+5^{1.5})	\frac{d}{dx}((6x+5)^{1.5})
integral from-1 to 3 of (3x^2-2x+1)	\int\:_{-1}^{3}(3x^{2}-2x+1)dx
inverse oflaplace 3/(s^2-1)	inverselaplace\:\frac{3}{s^{2}-1}
limit as x approaches+(-2) of-2	\lim\:_{x\to\:+(-2)}(-2)
derivative of e^{x^{1/3}}	\frac{d}{dx}(e^{x^{\frac{1}{3}}})
integral from 2 to 3 of (35)/(sqrt(3-x))	\int\:_{2}^{3}\frac{35}{\sqrt{3-x}}dx
derivative of (s^6+1/s)^{5/2}	derivative\:(s^{6}+\frac{1}{s})^{\frac{5}{2}}
(\partial)/(\partial y)(sqrt(3x^2+8xy+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{3x^{2}+8xy+y^{2}})
integral of (2x+3)/(sqrt(2x+4))	\int\:\frac{2x+3}{\sqrt{2x+4}}dx
derivative of p(x)=x^3-5x^2-4x+20	derivative\:p(x)=x^{3}-5x^{2}-4x+20
derivative of sqrt(8+cos(t^2))	derivative\:\sqrt{8+\cos(t^{2})}
limit as x approaches (3pi)/2 of-2tan(x)	\lim\:_{x\to\:\frac{3π}{2}}(-2\tan(x))
integral of sin^2(7x)	\int\:\sin^{2}(7x)dx
(\partial)/(\partial x)(3x^{3y})	\frac{\partial\:}{\partial\:x}(3x^{3y})
y^{''}+y^'+3y=0,y(0)=1,y^'(0)=2	y^{\prime\:\prime\:}+y^{\prime\:}+3y=0,y(0)=1,y^{\prime\:}(0)=2
limit as x approaches infinity of e^{3x}	\lim\:_{x\to\:\infty\:}(e^{3x})
e^yy^'=x^2	e^{y}y^{\prime\:}=x^{2}
integral of sqrt(576-16x^2)	\int\:\sqrt{576-16x^{2}}dx
(2y^2+2y+4x^2)dx+(2xy+x)dy=0	(2y^{2}+2y+4x^{2})dx+(2xy+x)dy=0
slope of 2-3/(x^2),\at x=1	slope\:2-\frac{3}{x^{2}},\at\:x=1
tangent of f(x)= 7/(sqrt(x)),(1,7)	tangent\:f(x)=\frac{7}{\sqrt{x}},(1,7)
limit as x approaches 0+of x-ln(x)	\lim\:_{x\to\:0+}(x-\ln(x))
(\partial)/(\partial x)((x^3)/(1-x^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{3}}{1-x^{2}})
integral from-pi to pi of sin(x)cos(nx)	\int\:_{-π}^{π}\sin(x)\cos(nx)dx
2t((dy)/(dt))+y=4t^2+3t	2t(\frac{dy}{dt})+y=4t^{2}+3t
integral from 2 to 3 of 5/(x^2-1)	\int\:_{2}^{3}\frac{5}{x^{2}-1}dx
integral of 1/(sqrt(e^x))	\int\:\frac{1}{\sqrt{e^{x}}}dx
(dx)/(dt)=2x	\frac{dx}{dt}=2x
limit as x approaches infinity of (sqrt(1+\sqrt{1/x)}-1)sqrt(x)	\lim\:_{x\to\:\infty\:}((\sqrt{1+\sqrt{\frac{1}{x}}}-1)\sqrt{x})
y^'=e^{x-y}	y^{\prime\:}=e^{x-y}
integral from-2 to 2 of 5-sqrt(4-x^2)	\int\:_{-2}^{2}5-\sqrt{4-x^{2}}dx
integral of (-1)/(x+1)	\int\:\frac{-1}{x+1}dx
tangent of f(x)=x^2-2x-3	tangent\:f(x)=x^{2}-2x-3
(\partial)/(\partial x)(x^2e^{x+y}+2ycos(xy)-xy^2sin(xy))	\frac{\partial\:}{\partial\:x}(x^{2}e^{x+y}+2y\cos(xy)-xy^{2}\sin(xy))
area x^2, 2/((x^2+1))	area\:x^{2},\frac{2}{(x^{2}+1)}
(\partial)/(\partial x)(cos(x+7y))	\frac{\partial\:}{\partial\:x}(\cos(x+7y))
1/x (dy)/(dx)+2y-e^{-x^2}=0	\frac{1}{x}\frac{dy}{dx}+2y-e^{-x^{2}}=0
limit as x approaches 0 of (6/(x+6)-1)/x	\lim\:_{x\to\:0}(\frac{\frac{6}{x+6}-1}{x})
limit as x approaches 10 of-15	\lim\:_{x\to\:10}(-15)
derivative of y=3e^x	derivative\:y=3e^{x}
inverse oflaplace (0.1s)/(s^2+10s+9.8)	inverselaplace\:\frac{0.1s}{s^{2}+10s+9.8}
integral of 5xsqrt(x)+2	\int\:5x\sqrt{x}+2dx
derivative of 2(e^xcos(x-e^xsin(x)))	\frac{d}{dx}(2(e^{x}\cos(x)-e^{x}\sin(x)))
derivative of f(x)= 1/2 x-1/10	derivative\:f(x)=\frac{1}{2}x-\frac{1}{10}
derivative of f(x)= 4/3 pix^3	derivative\:f(x)=\frac{4}{3}πx^{3}
sum from k=5 to infinity of (k+7)/(k+6)	\sum\:_{k=5}^{\infty\:}\frac{k+7}{k+6}
derivative of (tan(x-3)/(sec(x)))	\frac{d}{dx}(\frac{\tan(x)-3}{\sec(x)})
derivative of f(x)=7x	derivative\:f(x)=7x
y^{''}+sqrt(80)y^'+20y=0	y^{\prime\:\prime\:}+\sqrt{80}y^{\prime\:}+20y=0
integral of ((-2u^4+3sqrt(u)))/(u^2)	\int\:\frac{(-2u^{4}+3\sqrt{u})}{u^{2}}du
limit as x approaches 1/4 of x^2+3x	\lim\:_{x\to\:\frac{1}{4}}(x^{2}+3x)
derivative of-(3e^{3/x}/(x^2))	\frac{d}{dx}(-\frac{3e^{\frac{3}{x}}}{x^{2}})
derivative of f(x)=21x^3ln(x)	derivative\:f(x)=21x^{3}\ln(x)
integral of (2x^4+2\sqrt[5]{x})/x	\int\:\frac{2x^{4}+2\sqrt[5]{x}}{x}dx
y^{''}+6y^'+9y=3t+5	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=3t+5
integral of (4x^3-3x^2+5)	\int\:(4x^{3}-3x^{2}+5)dx
(dy)/(dx)=(x+y^2)/(2y)	\frac{dy}{dx}=\frac{x+y^{2}}{2y}
tangent of y=2x^3-8x	tangent\:y=2x^{3}-8x
integral of (e^z+1)/(e^z+z)	\int\:\frac{e^{z}+1}{e^{z}+z}dz
integral of (2x+4)^2+sqrt(2x+2)	\int\:(2x+4)^{2}+\sqrt{2x+2}dx
limit as t approaches 0 of 4/t-4/(t^2+t)	\lim\:_{t\to\:0}(\frac{4}{t}-\frac{4}{t^{2}+t})
integral of (cos^5(t))/(sqrt(sin(t)))	\int\:\frac{\cos^{5}(t)}{\sqrt{\sin(t)}}dt
derivative of sqrt(10+\sqrt{3x)}	\frac{d}{dx}(\sqrt{10+\sqrt{3x}})
derivative of y^2-xsin(y-xye^{-y})	\frac{d}{dx}(y^{2}-x\sin(y)-xye^{-y})
integral of sqrt((1+x^2))	\int\:\sqrt{(1+x^{2})}dx
derivative of x/(3-{z(x)})	\frac{d}{dx}(\frac{x}{3-{z}(x)})
slope ofintercept (3)(7.8)	slopeintercept\:(3)(7.8)
limit as x approaches-infinity of 2x	\lim\:_{x\to\:-\infty\:}(2x)
integral of-k/x	\int\:-\frac{k}{x}dx
integral from 1 to 2 of (5x^4+5)	\int\:_{1}^{2}(5x^{4}+5)dx
(d^2)/(dx^2)((5x^2-4x)cos(x))	\frac{d^{2}}{dx^{2}}((5x^{2}-4x)\cos(x))
taylor f(x)=(x-ln(1+x))/(x^2)	taylor\:f(x)=\frac{x-\ln(1+x)}{x^{2}}
maclaurin 2e^{-x/2}+e^{-x}	maclaurin\:2e^{-\frac{x}{2}}+e^{-x}
limit as x approaches+pi/2+of e^{sec(x)}	\lim\:_{x\to\:+\frac{π}{2}+}(e^{\sec(x)})

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