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Popular Calculus Problems

area x^2-1,x+1	area\:x^{2}-1,x+1
integral from 2 to 6 of (x^3+x)	\int\:_{2}^{6}(x^{3}+x)dx
integral of e^{x^2+8x}	\int\:e^{x^{2}+8x}dx
integral of sin(1/5)x	\int\:\sin(\frac{1}{5})xdx
sum from n=0 to infinity of (cos^2(5))^n	\sum\:_{n=0}^{\infty\:}(\cos^{2}(5))^{n}
(dy)/(dx)=(y-1)^2x^3	\frac{dy}{dx}=(y-1)^{2}x^{3}
integral of 32x	\int\:32xdx
derivative of 1/(5x^2+4x)	\frac{d}{dx}(\frac{1}{5x^{2}+4x})
derivative of (40ln(3x+1))-(x/3)	derivative\:(40\ln(3x+1))-(\frac{x}{3})
limit as x approaches 1 of (2x^2)-5x+1	\lim\:_{x\to\:1}((2x^{2})-5x+1)
integral of ((4x^2+x+4))/((x^2+1)^2)	\int\:\frac{(4x^{2}+x+4)}{(x^{2}+1)^{2}}dx
integral of e^x(1+x)	\int\:e^{x}(1+x)dx
d/(du)(ucos(v))	\frac{d}{du}(u\cos(v))
integral of 4/(x^2+1)	\int\:\frac{4}{x^{2}+1}dx
integral of (3x^2+1)^3x	\int\:(3x^{2}+1)^{3}xdx
limit as x approaches-1 of x/(x^2+1)	\lim\:_{x\to\:-1}(\frac{x}{x^{2}+1})
integral from 0 to 6 of sqrt(2x+1)	\int\:_{0}^{6}\sqrt{2x+1}dx
limit as x approaches 0 of sin(x)*1/x	\lim\:_{x\to\:0}(\sin(x)\cdot\:\frac{1}{x})
derivative of ((2x/(x+2))^4)	\frac{d}{dx}((\frac{2x}{x+2})^{4})
limit as x approaches 8 of ((x+6))/(x-8)	\lim\:_{x\to\:8}(\frac{(x+6)}{x-8})
integral of (x^2)/((5+x^3)^2)	\int\:\frac{x^{2}}{(5+x^{3})^{2}}dx
derivative of f(x)=-2cos(x)	derivative\:f(x)=-2\cos(x)
integral of sqrt(x)-2/(sqrt(x))	\int\:\sqrt{x}-\frac{2}{\sqrt{x}}dx
limit as x approaches 16 of sqrt(x^2-9)	\lim\:_{x\to\:16}(\sqrt{x^{2}-9})
integral of tan^5(1)	\int\:\tan^{5}(1)dx
(\partial)/(\partial y)(ln(3x+2y))	\frac{\partial\:}{\partial\:y}(\ln(3x+2y))
limit as x approaches 0+of (x+1)^{ln(x)}	\lim\:_{x\to\:0+}((x+1)^{\ln(x)})
derivative of ln(e^{4x+1})	\frac{d}{dx}(\ln(e^{4x+1}))
(\partial)/(\partial x)((5xy)/(10x-y))	\frac{\partial\:}{\partial\:x}(\frac{5xy}{10x-y})
limit as x approaches pi/2 of xsec(x)	\lim\:_{x\to\:\frac{π}{2}}(x\sec(x))
inverse oflaplace 4/(s(s+2)^3)	inverselaplace\:\frac{4}{s(s+2)^{3}}
integral of e^{ln(t)}	\int\:e^{\ln(t)}dt
integral of-cot(x)	\int\:-\cot(x)dx
integral of (35)/(x^3-27)	\int\:\frac{35}{x^{3}-27}dx
area y=x^3-10x^2+16x,y=-x^3+10x^2-16x	area\:y=x^{3}-10x^{2}+16x,y=-x^{3}+10x^{2}-16x
limit as x approaches 0 of x^2e^{cos(1/x)}	\lim\:_{x\to\:0}(x^{2}e^{\cos(\frac{1}{x})})
integral of cos(x)+1/4 x	\int\:\cos(x)+\frac{1}{4}xdx
integral of 1/(y-y^3)	\int\:\frac{1}{y-y^{3}}dy
integral from 0 to 4 of 2pi(x)(4x-x^2)	\int\:_{0}^{4}2π(x)(4x-x^{2})dx
derivative of 1/(x^{-5})	\frac{d}{dx}(\frac{1}{x^{-5}})
2× 2+6× 1/22× 2	2\times\:2+6\times\:1/22\times\:2
(\partial)/(\partial x)(y^{-2}(4y+9x^2))	\frac{\partial\:}{\partial\:x}(y^{-2}(4y+9x^{2}))
derivative of f(x)=(x^3+x)^6	derivative\:f(x)=(x^{3}+x)^{6}
(\partial)/(\partial x)(sin(3t))	\frac{\partial\:}{\partial\:x}(\sin(3t))
f(x)=cos(x^4)	f(x)=\cos(x^{4})
(\partial}{\partial s}(\frac{(r+s))/t)	\frac{\partial\:}{\partial\:s}(\frac{(r+s)}{t})
tangent of y=7ln((e^x+e^{-x})/2),(0,0)	tangent\:y=7\ln(\frac{e^{x}+e^{-x}}{2}),(0,0)
derivative of (x^2-2x+2e^x)	\frac{d}{dx}((x^{2}-2x+2)e^{x})
integral of 15sqrt(x)+3/(sqrt(x))	\int\:15\sqrt{x}+\frac{3}{\sqrt{x}}dx
x(dy)/(dx)=y^2+1	x\frac{dy}{dx}=y^{2}+1
integral of (1/(4+x^2))	\int\:(\frac{1}{4+x^{2}})dx
((x^2)/(x^2-x-2))^'	(\frac{x^{2}}{x^{2}-x-2})^{\prime\:}
inverse oflaplace (2s-3)/((s+4)(s-3)^3)	inverselaplace\:\frac{2s-3}{(s+4)(s-3)^{3}}
integral of (15x^4)/(x^5+7)	\int\:\frac{15x^{4}}{x^{5}+7}dx
integral of (sin(20t))/(sin(10t))	\int\:\frac{\sin(20t)}{\sin(10t)}dx
integral of 3x^5-5x^9	\int\:3x^{5}-5x^{9}dx
dy=2t(y^2+9)dt	dy=2t(y^{2}+9)dt
sum from n=1 to infinity of 1/(n^{4/3)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{\frac{4}{3}}}
(\partial)/(\partial x)(3x+6y)	\frac{\partial\:}{\partial\:x}(3x+6y)
limit as x approaches 0-of 3/(x^2)	\lim\:_{x\to\:0-}(\frac{3}{x^{2}})
area y=x^2,y=x+2,y=0	area\:y=x^{2},y=x+2,y=0
derivative of 6sqrt(t)-4t^3+9	derivative\:6\sqrt{t}-4t^{3}+9
integral of (16x^3)/(sqrt(4-x^2))	\int\:\frac{16x^{3}}{\sqrt{4-x^{2}}}dx
integral of-x+4	\int\:-x+4dx
integral of xsin(3)x^2	\int\:x\sin(3)x^{2}dx
y^'-4y=0	y^{\prime\:}-4y=0
integral of xcos(8x)	\int\:x\cos(8x)dx
limit as x approaches 4-of (5x)/(x^2-4x)	\lim\:_{x\to\:4-}(\frac{5x}{x^{2}-4x})
integral of (15)/(1-cos(5x))	\int\:\frac{15}{1-\cos(5x)}dx
sum from n=1 to infinity of (7n)/(6n+1)	\sum\:_{n=1}^{\infty\:}\frac{7n}{6n+1}
derivative of 6x^5	derivative\:6x^{5}
integral of (sec(θ)tan(θ))/(sec^2(θ)-sec(θ))	\int\:\frac{\sec(θ)\tan(θ)}{\sec^{2}(θ)-\sec(θ)}dθ
integral of (a+x-x^2)	\int\:(a+x-x^{2})dx
integral of 7x^{2/5}+8x^{-4/5}	\int\:7x^{\frac{2}{5}}+8x^{-\frac{4}{5}}dx
(\partial)/(\partial x)(((2x-y))/(5x+3y))	\frac{\partial\:}{\partial\:x}(\frac{(2x-y)}{5x+3y})
x^2y^{''}+xy^'-y=ln(x)	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-y=\ln(x)
integral of x/(1-2x^2)	\int\:\frac{x}{1-2x^{2}}dx
integral from 2 to 4 of x^2	\int\:_{2}^{4}x^{2}dx
integral from 1 to 4 of (3x^3+x+1)	\int\:_{1}^{4}(3x^{3}+x+1)dx
derivative of 3/(8x^{5/2})	\frac{d}{dx}(\frac{3}{8x^{\frac{5}{2}}})
(\partial)/(\partial θ)(ρcos(φ))	\frac{\partial\:}{\partial\:θ}(ρ\cos(φ))
limit as x approaches 5 of 2x-3x+4	\lim\:_{x\to\:5}(2x-3x+4)
integral of (y^2+38y+361)/((y^2+361)^2)	\int\:\frac{y^{2}+38y+361}{(y^{2}+361)^{2}}dy
limit as x approaches 2 of 2x^2-2x	\lim\:_{x\to\:2}(2x^{2}-2x)
integral of x^2cot(x^3)	\int\:x^{2}\cot(x^{3})dx
tangent of 3x+5/x	tangent\:3x+\frac{5}{x}
derivative of-x/((1-x^2^{3/2)})	\frac{d}{dx}(-\frac{x}{(1-x^{2})^{\frac{3}{2}}})
tangent of f(x)=x^2-1,(-1,0)	tangent\:f(x)=x^{2}-1,(-1,0)
integral of 3x^2+1	\int\:3x^{2}+1dx
derivative of 3/(\sqrt[3]{x^4})	\frac{d}{dx}(\frac{3}{\sqrt[3]{x^{4}}})
derivative of x/(sqrt(x^2+1)-1)	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+1}}-1)
(dy)/(dx)=(x^2y-y)/(y+1)	\frac{dy}{dx}=\frac{x^{2}y-y}{y+1}
integral of 1/18 x	\int\:\frac{1}{18}xdx
derivative of-4x^3-sin(x)	\frac{d}{dx}(-4x^{3}-\sin(x))
limit as x approaches 1 of \|x+1\|	\lim\:_{x\to\:1}(\left\|x+1\right\|)
integral of ((e^{-1/x}))/(x^2)	\int\:\frac{(e^{-\frac{1}{x}})}{x^{2}}dx
integral of (cos(x))/((sin(x)-1)^2)	\int\:\frac{\cos(x)}{(\sin(x)-1)^{2}}dx
(\partial)/(\partial x)(x^2+y^2(1-x)^3)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}(1-x)^{3})
(\partial)/(\partial x)(x/(1-x))	\frac{\partial\:}{\partial\:x}(\frac{x}{1-x})
integral of (x^2-16)/(x-4)	\int\:\frac{x^{2}-16}{x-4}dx

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