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Popular Calculus Problems

area y=2sqrt(x),y= x/2	area\:y=2\sqrt{x},y=\frac{x}{2}
limit as x approaches-6 of (x^2+8)/(x+6)	\lim\:_{x\to\:-6}(\frac{x^{2}+8}{x+6})
derivative of (cos(ln(x))/x)	\frac{d}{dx}(\frac{\cos(\ln(x))}{x})
limit as x approaches 3 of 3x-3ax+2a	\lim\:_{x\to\:3}(3x-3ax+2a)
derivative of x^3-3x^2-24x+80	\frac{d}{dx}(x^{3}-3x^{2}-24x+80)
integral of (x^5)/(sqrt(1+x^3))	\int\:\frac{x^{5}}{\sqrt{1+x^{3}}}dx
integral of-75x^2+600x+C	\int\:-75x^{2}+600x+Cdx
integral of x^2sqrt(3+x^3)	\int\:x^{2}\sqrt{3+x^{3}}dx
(x^2+y)dx+(x+e^y)dy=0	(x^{2}+y)dx+(x+e^{y})dy=0
integral from 0 to ln(2) of 2/(e^x+3)	\int\:_{0}^{\ln(2)}\frac{2}{e^{x}+3}dx
derivative of 2te^{-t}	derivative\:2te^{-t}
slope of (1,-4),(4,-5)	slope\:(1,-4),(4,-5)
integral of cos(pi)	\int\:\cos(π)
limit as x approaches 3+of 1/(x^2-9)	\lim\:_{x\to\:3+}(\frac{1}{x^{2}-9})
derivative of (3x/((x^2+1)^{3/5)})	\frac{d}{dx}(\frac{3x}{(x^{2}+1)^{\frac{3}{5}}})
taylor (x^2-2x+4),2	taylor\:(x^{2}-2x+4),2
integral of 1/(x^2sqrt(4x^2-1))	\int\:\frac{1}{x^{2}\sqrt{4x^{2}-1}}dx
x(dy)/(dx)=y+(x^2+y^2)^{1/2}	x\frac{dy}{dx}=y+(x^{2}+y^{2})^{\frac{1}{2}}
tangent of f(x)=2x^2+x-1,\at a=-2	tangent\:f(x)=2x^{2}+x-1,\at\:a=-2
integral of e^xxcos(x)	\int\:e^{x}x\cos(x)dx
f(x)=1-2x	f(x)=1-2x
limit as x approaches 6 of sqrt(x^3+4x)	\lim\:_{x\to\:6}(\sqrt{x^{3}+4x})
derivative of ln(x^7sin^2(x))	\frac{d}{dx}(\ln(x^{7}\sin^{2}(x)))
integral of 1/(x^2sqrt(x^2+a^2))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+a^{2}}}dx
integral of xsqrt(49-x^2)	\int\:x\sqrt{49-x^{2}}dx
integral of (2x+3/(x^2)-6/(x^4))	\int\:(2x+\frac{3}{x^{2}}-\frac{6}{x^{4}})dx
derivative of sin(x(1+cos(x)))	\frac{d}{dx}(\sin(x)(1+\cos(x)))
derivative of sin(3x+4y)	\frac{d}{dx}(\sin(3x+4y))
derivative of x^3+2x^2+x	\frac{d}{dx}(x^{3}+2x^{2}+x)
derivative of cos^2(z)	derivative\:\cos^{2}(z)
integral of 7x^5e^{-x^3}	\int\:7x^{5}e^{-x^{3}}dx
integral of x(y)	\int\:x(y)dx
derivative of x^4ln(x-1/3 x^3)	\frac{d}{dx}(x^{4}\ln(x)-\frac{1}{3}x^{3})
area x^2-x,x	area\:x^{2}-x,x
derivative of G(t)=sqrt(5t)+(sqrt(7))/t	derivative\:G(t)=\sqrt{5t}+\frac{\sqrt{7}}{t}
derivative of f(x)=(6x+8x^2)/((3+8x)^2)	derivative\:f(x)=\frac{6x+8x^{2}}{(3+8x)^{2}}
integral from-1 to 1 of pi(x^2+1)^2	\int\:_{-1}^{1}π(x^{2}+1)^{2}dx
integral of (6x^5-12x^4+9x^3)/(3x^2)	\int\:\frac{6x^{5}-12x^{4}+9x^{3}}{3x^{2}}dx
(dy)/(dx)=2yx+yx^2	\frac{dy}{dx}=2yx+yx^{2}
integral of 7θcos(θ)	\int\:7θ\cos(θ)dθ
derivative of x(4-x^2)	\frac{d}{dx}(x(4-x^{2}))
-x(dy)/(dx)=x^2-y	-x\frac{dy}{dx}=x^{2}-y
limit as x approaches 0 of 3/(x(2*x+1))	\lim\:_{x\to\:0}(\frac{3}{x(2\cdot\:x+1)})
(\partial)/(\partial x)(x^3+y^3-6xy)	\frac{\partial\:}{\partial\:x}(x^{3}+y^{3}-6xy)
integral of sec^2(3x-4)	\int\:\sec^{2}(3x-4)dx
sum from n=0 to infinity of sqrt(n)	\sum\:_{n=0}^{\infty\:}\sqrt{n}
integral of 1-cos^2(2x)	\int\:1-\cos^{2}(2x)dx
derivative of R(x)=71sqrt(x)	derivative\:R(x)=71\sqrt{x}
integral of 3/(5ysqrt(y^2-1))	\int\:\frac{3}{5y\sqrt{y^{2}-1}}dy
derivative of-(sqrt(1-x)/2)	\frac{d}{dx}(-\frac{\sqrt{1-x}}{2})
tangent of 8e^x+x	tangent\:8e^{x}+x
limit as x approaches-1 of x/(1-x^4)	\lim\:_{x\to\:-1}(\frac{x}{1-x^{4}})
integral from 0 to 1 of (1+r)^3	\int\:_{0}^{1}(1+r)^{3}dr
inverse oflaplace s*+5	inverselaplace\:s\cdot\:+5
limit as x approaches 2 of (x-1)/(x^2-1)	\lim\:_{x\to\:2}(\frac{x-1}{x^{2}-1})
integral of x^4(ln(x))^2	\int\:x^{4}(\ln(x))^{2}dx
integral of 9/(sqrt(x))+9sqrt(x)	\int\:\frac{9}{\sqrt{x}}+9\sqrt{x}dx
integral of 1/((x-3)^2)	\int\:\frac{1}{(x-3)^{2}}dx
tangent of y=2sin(pix-y),(1,0)	tangent\:y=2\sin(πx-y),(1,0)
integral of \sqrt[5]{tan(x)}sec^4(x)	\int\:\sqrt[5]{\tan(x)}\sec^{4}(x)dx
y^{''}-5y^'+6y=e^{6x}	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=e^{6x}
integral of sin(x)e^x	\int\:\sin(x)e^{x}dx
derivative of f(x)=(\sqrt[7]{x})^{ln(x)}	derivative\:f(x)=(\sqrt[7]{x})^{\ln(x)}
derivative of e^{5t}	derivative\:e^{5t}
integral of (x^3+2)^{1/2}*x^2	\int\:(x^{3}+2)^{\frac{1}{2}}\cdot\:x^{2}dx
derivative of sec^2(5x^2)	\frac{d}{dx}(\sec^{2}(5x^{2}))
(\partial)/(\partial x)(2x^2y-y^3+x)	\frac{\partial\:}{\partial\:x}(2x^{2}y-y^{3}+x)
integral from 0 to 1 of 2pix(x^5-x^6)	\int\:_{0}^{1}2πx(x^{5}-x^{6})dx
integral of 1/(e^{2y)}	\int\:\frac{1}{e^{2y}}dy
x(dy)/(dx)+2y=x^3-x	x\frac{dy}{dx}+2y=x^{3}-x
integral from 0 to pi of tcos^2(t)	\int\:_{0}^{π}t\cos^{2}(t)dt
integral of sin((npix)/1)	\int\:\sin(\frac{nπx}{1})dx
limit as x approaches 1+of x+1	\lim\:_{x\to\:1+}(x+1)
limit as x approaches 1 of (x^2+1)/(x-2)	\lim\:_{x\to\:1}(\frac{x^{2}+1}{x-2})
integral of (cos(θ))/(sqrt(1-sin(θ)))	\int\:\frac{\cos(θ)}{\sqrt{1-\sin(θ)}}dθ
tangent of y=6ln(x^2),(e,12)	tangent\:y=6\ln(x^{2}),(e,12)
tangent of f(x)=e^xsin(x),(0,0)	tangent\:f(x)=e^{x}\sin(x),(0,0)
derivative of y=(3+7x-8sqrt(x))/x	derivative\:y=\frac{3+7x-8\sqrt{x}}{x}
(x^2e^{x+3})^'	(x^{2}e^{x+3})^{\prime\:}
y^'=-3y+e^{-2x},y(0)=0	y^{\prime\:}=-3y+e^{-2x},y(0)=0
area f(x)= 2/(1+x^2),h(x)=x^2	area\:f(x)=\frac{2}{1+x^{2}},h(x)=x^{2}
(dy}{dx}=(\frac{(xy)^2)/8+y^2)	\frac{dy}{dx}=(\frac{(xy)^{2}}{8}+y^{2})
(d^2)/(dx^2)(ln(x))	\frac{d^{2}}{dx^{2}}(\ln(x))
y^{''}+4.5y^'=0	y^{\prime\:\prime\:}+4.5y^{\prime\:}=0
integral of x+4-4/x	\int\:x+4-\frac{4}{x}dx
derivative of (2t+t)/(t+3)	derivative\:\frac{2t+t}{t+3}
derivative of xsin(xtan(x))	\frac{d}{dx}(x\sin(x)\tan(x))
derivative of (x^{3/2}-4x(x^4-3/(x^2)+2))	\frac{d}{dx}((x^{\frac{3}{2}}-4x)(x^{4}-\frac{3}{x^{2}}+2))
derivative of sqrt(4x+2)	derivative\:\sqrt{4x+2}
derivative of (2x^2+5x+8/(2x^2))	\frac{d}{dx}(\frac{2x^{2}+5x+8}{2x^{2}})
integral of 1/((sec(x))^2)	\int\:\frac{1}{(\sec(x))^{2}}dx
derivative of f(x)=3e^x	derivative\:f(x)=3e^{x}
inverse oflaplace 1/(s^2+8s+16)	inverselaplace\:\frac{1}{s^{2}+8s+16}
derivative of 1/(x+a)	\frac{d}{dx}(\frac{1}{x+a})
integral of (1/(\sqrt[3]{x)})	\int\:(\frac{1}{\sqrt[3]{x}})dx
taylor 1/(x-1)	taylor\:\frac{1}{x-1}
integral of ln(e^{2x-1})	\int\:\ln(e^{2x-1})dx
(\partial)/(\partial x)(2x+2y^2)	\frac{\partial\:}{\partial\:x}(2x+2y^{2})
taylor xsin(x^3)	taylor\:x\sin(x^{3})
derivative of x^{-2/4}+x^{2/4}	derivative\:x^{-\frac{2}{4}}+x^{\frac{2}{4}}

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