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Popular Calculus Problems

(\partial)/(\partial y)(arctan(y))	\frac{\partial\:}{\partial\:y}(\arctan(y))
area y=x^2+3,(-2,4)	area\:y=x^{2}+3,(-2,4)
derivative of 4^{9-x^2}	\frac{d}{dx}(4^{9-x^{2}})
integral of 1/(1+y^2)	\int\:\frac{1}{1+y^{2}}dy
limit as x approaches 0 of (x^2-4)/(x-2)	\lim\:_{x\to\:0}(\frac{x^{2}-4}{x-2})
limit as x approaches 0 of sqrt(x)+x+x^2	\lim\:_{x\to\:0}(\sqrt{x}+x+x^{2})
(dy)/(dx)=9x^2	\frac{dy}{dx}=9x^{2}
laplacetransform x*sin(x)	laplacetransform\:x\cdot\:\sin(x)
y^{''}-12y^'+36y=0,y(0)=1,y(1)=0	y^{\prime\:\prime\:}-12y^{\prime\:}+36y=0,y(0)=1,y(1)=0
integral of (x^2)/((x-3)^3)	\int\:\frac{x^{2}}{(x-3)^{3}}dx
(d^2y)/(dx^2)+(dy)/(dx)=0	\frac{d^{2}y}{dx^{2}}+\frac{dy}{dx}=0
tangent of f(x)=x^3-7x^2,\at x=0	tangent\:f(x)=x^{3}-7x^{2},\at\:x=0
integral of (x^6)/(sqrt(x^{14)-7)}	\int\:\frac{x^{6}}{\sqrt{x^{14}-7}}dx
integral of 4cos^5(x)sin^4(x)	\int\:4\cos^{5}(x)\sin^{4}(x)dx
limit as x approaches 8-of 7x-7	\lim\:_{x\to\:8-}(7x-7)
x^2y^{''}-2y^'=0	x^{2}y^{\prime\:\prime\:}-2y^{\prime\:}=0
integral of (cos(x))	\int\:(\cos(x))dx
integral of 1/(xsqrt(x^4-1))	\int\:\frac{1}{x\sqrt{x^{4}-1}}dx
derivative of f(x)=ln(4sin^2(x))	derivative\:f(x)=\ln(4\sin^{2}(x))
integral of e^{-x}*1/x	\int\:e^{-x}\cdot\:\frac{1}{x}dx
derivative of-2sin(θ)	derivative\:-2\sin(θ)
derivative of x^{8sin(x})	\frac{d}{dx}(x^{8\sin(x)})
(dy)/(dx)=y^4	\frac{dy}{dx}=y^{4}
(\partial)/(\partial y)(sin(pi(4x-6y)))	\frac{\partial\:}{\partial\:y}(\sin(π(4x-6y)))
limit as x approaches 0 of 1/(x^4)	\lim\:_{x\to\:0}(\frac{1}{x^{4}})
d/(dy)(2y^2)	\frac{d}{dy}(2y^{2})
inverse oflaplace 1/((s^2+6s+25))	inverselaplace\:\frac{1}{(s^{2}+6s+25)}
integral of 4sin(t)	\int\:4\sin(t)dt
y^{''}+9y=t^2e^{3t}+6	y^{\prime\:\prime\:}+9y=t^{2}e^{3t}+6
(\partial)/(\partial y)(xysin(z))	\frac{\partial\:}{\partial\:y}(xy\sin(z))
limit as x approaches 0 of (e^{-1/x})/x	\lim\:_{x\to\:0}(\frac{e^{-\frac{1}{x}}}{x})
integral from 3 to 3.5 of x/8	\int\:_{3}^{3.5}\frac{x}{8}dx
limit as x approaches 2 of x^3-3^x	\lim\:_{x\to\:2}(x^{3}-3^{x})
derivative of r^2	derivative\:r^{2}
y^{''}-4y=4xe^{-2x}	y^{\prime\:\prime\:}-4y=4xe^{-2x}
(dy)/(dx)=2tan^2(x)	\frac{dy}{dx}=2\tan^{2}(x)
integral from-1 to 1 of e^{-x^2}	\int\:_{-1}^{1}e^{-x^{2}}dx
limit as x approaches 0 of x^{1/(ln(x))}	\lim\:_{x\to\:0}(x^{\frac{1}{\ln(x)}})
integral of 3cos(n)x	\int\:3\cos(n)xdx
sum from n=1 to infinity of 2/(1+e^n)	\sum\:_{n=1}^{\infty\:}\frac{2}{1+e^{n}}
derivative of ((sqrt(x)-3)/(sqrt(x)+3))	\frac{d}{dx}(\frac{(\sqrt{x}-3)}{\sqrt{x}+3})
integral from 0 to 4 of (e^{-0.25x}+5)	\int\:_{0}^{4}(e^{-0.25x}+5)dx
inverse oflaplace 1/((s^2+1)(s^2))	inverselaplace\:\frac{1}{(s^{2}+1)(s^{2})}
limit as x approaches 0+of arccot(x)	\lim\:_{x\to\:0+}(\arccot(x))
integral of (2x^2+3x-3)(5x+3)	\int\:(2x^{2}+3x-3)(5x+3)dx
derivative of f(x)=(x^4)/8-8x	derivative\:f(x)=\frac{x^{4}}{8}-8x
limit as x approaches infinity of 5+1/x	\lim\:_{x\to\:\infty\:}(5+\frac{1}{x})
limit as x approaches 3 of 4+4(-4)	\lim\:_{x\to\:3}(4+4(-4))
integral of 7xe^{-2x}	\int\:7xe^{-2x}dx
derivative of cos((x^2+6^5))	\frac{d}{dx}(\cos((x^{2}+6)^{5}))
derivative of e^xx^2+4e^xx+2e^x	\frac{d}{dx}(e^{x}x^{2}+4e^{x}x+2e^{x})
integral of 7e^xsqrt(3+e^x)	\int\:7e^{x}\sqrt{3+e^{x}}dx
integral of r^5	\int\:r^{5}dr
limit as x approaches 0 of cosh(x)	\lim\:_{x\to\:0}(\cosh(x))
(dy)/(dx)=(x/(sqrt(1-6x^2)))	\frac{dy}{dx}=(\frac{x}{\sqrt{1-6x^{2}}})
integral of (10x^3+7/(x^2)-x)	\int\:(10x^{3}+\frac{7}{x^{2}}-x)dx
integral of 2xcos(x)-cos^2(x)	\int\:2x\cos(x)-\cos^{2}(x)dx
integral from 0 to 2 of 2/(sqrt(16-x^2))	\int\:_{0}^{2}\frac{2}{\sqrt{16-x^{2}}}dx
integral of cot^3(4x)	\int\:\cot^{3}(4x)dx
tangent of f(x)=(4x)/(x+2),\at x=6	tangent\:f(x)=\frac{4x}{x+2},\at\:x=6
derivative of \sqrt[3]{x+8}	\frac{d}{dx}(\sqrt[3]{x+8})
integral of cos^2(xta)n^3x	\int\:\cos^{2}(xta)n^{3}xdx
derivative of sqrt(3)u+sqrt(5u)	derivative\:\sqrt{3}u+\sqrt{5u}
y^'=4-9^2-6x^5	y^{\prime\:}=4-9^{2}-6x^{5}
derivative of 1/(\sqrt[4]{x^5})	\frac{d}{dx}(\frac{1}{\sqrt[4]{x^{5}}})
integral from 0 to 6 of sqrt(36-x^2)	\int\:_{0}^{6}\sqrt{36-x^{2}}dx
integral of (33)/(33+e^x)	\int\:\frac{33}{33+e^{x}}dx
integral of ((x^2-1))/x	\int\:\frac{(x^{2}-1)}{x}dx
derivative of ln(x^2+1-e^{x/2}cos(pix))	\frac{d}{dx}(\ln(x^{2}+1)-e^{\frac{x}{2}}\cos(πx))
integral of (4x+5)/(x^2+4x+2)	\int\:\frac{4x+5}{x^{2}+4x+2}dx
integral of 1/(sqrt(x^2-x))	\int\:\frac{1}{\sqrt{x^{2}-x}}dx
(dy)/(dx)=(((2y+3))/((4x+5)))^2	\frac{dy}{dx}=(\frac{(2y+3)}{(4x+5)})^{2}
area cos(6x),0	area\:\cos(6x),0
y^{''}+4sqrt(3)y^'+12y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4\sqrt{3}y^{\prime\:}+12y=0,y(0)=1,y^{\prime\:}(0)=0
sum from n=1 to infinity of 2/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{2}{n+1}
integral from 0 to pi of x+sin(x)	\int\:_{0}^{π}x+\sin(x)dx
integral from 0 to 1 of x^2e^{-2x}	\int\:_{0}^{1}x^{2}e^{-2x}dx
derivative of 1/(sqrt(x^2+a^2))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}+a^{2}}})
integral of (x^2+2x+1)/(x^2)	\int\:\frac{x^{2}+2x+1}{x^{2}}dx
taylor sin(x),3	taylor\:\sin(x),3
limit as x approaches 2 of sqrt(4x+1)	\lim\:_{x\to\:2}(\sqrt{4x+1})
integral of 1/(sqrt((1+x^2)^3))	\int\:\frac{1}{\sqrt{(1+x^{2})^{3}}}dx
limit as x approaches-3 of x^2+7x+12	\lim\:_{x\to\:-3}(x^{2}+7x+12)
integral of x/(sqrt(5x^2+3))	\int\:\frac{x}{\sqrt{5x^{2}+3}}dx
derivative of (6-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{6-\sec(x)}{\tan(x)})
(\partial)/(\partial x)(-6y^3sin(6x))	\frac{\partial\:}{\partial\:x}(-6y^{3}\sin(6x))
tangent of f(x)=xe^x,\at x=1	tangent\:f(x)=xe^{x},\at\:x=1
integral of 36(4x+4)^2-2sqrt(3x-1)	\int\:36(4x+4)^{2}-2\sqrt{3x-1}dx
integral of 2csc(2x)	\int\:2\csc(2x)dx
limit as x approaches 0+of (\|x-4\|)/(x-4)	\lim\:_{x\to\:0+}(\frac{\left\|x-4\right\|}{x-4})
integral of (3x^2-8x+3)	\int\:(3x^{2}-8x+3)dx
integral of x^2sqrt(7x-5)	\int\:x^{2}\sqrt{7x-5}dx
t^3(dy)/(dt)+4t^2y=e^{-t}	t^{3}\frac{dy}{dt}+4t^{2}y=e^{-t}
integral of (tsqrt(t)+sqrt(t))/(t^2)	\int\:\frac{t\sqrt{t}+\sqrt{t}}{t^{2}}dt
R(a)=(3a+1)^2	R(a)=(3a+1)^{2}
y^'+4y=t^2e^{-4t}	y^{\prime\:}+4y=t^{2}e^{-4t}
integral of (2x+7)/(sqrt(9-4x^2))	\int\:\frac{2x+7}{\sqrt{9-4x^{2}}}dx
integral from 6 to 8 of (60)/((x-6)^3)	\int\:_{6}^{8}\frac{60}{(x-6)^{3}}dx
tangent of y=ln(x),\at x=2	tangent\:y=\ln(x),\at\:x=2
inverse oflaplace s/((s^2+1^2)^2)	inverselaplace\:\frac{s}{(s^{2}+1^{2})^{2}}

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