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Popular Calculus Problems
limit as x approaches 0+of ln(2/(x^2))
\lim\:_{x\to\:0+}(\ln(\frac{2}{x^{2}}))
integral from 0 to pi/2 of 4sin^2(3x)
\int\:_{0}^{\frac{π}{2}}4\sin^{2}(3x)dx
expand 3/(x(x+1)^2)
expand\:\frac{3}{x(x+1)^{2}}
integral of ((8x^3+3))/((x^2+2)^2)
\int\:\frac{(8x^{3}+3)}{(x^{2}+2)^{2}}dx
integral of (3x+2)^2
\int\:(3x+2)^{2}dx
(\partial}{\partial x}(-\frac{2x)/y)
\frac{\partial\:}{\partial\:x}(-\frac{2x}{y})
area y=4x-x^2,y=-6x
area\:y=4x-x^{2},y=-6x
limit as x approaches 8 of x^2-64
\lim\:_{x\to\:8}(x^{2}-64)
derivative of (e^x/(e^{2x)+1})
\frac{d}{dx}(\frac{e^{x}}{e^{2x}+1})
integral of xsqrt(x^2-1)
\int\:x\sqrt{x^{2}-1}dx
integral from 1 to 32 of x^{-6/5}
\int\:_{1}^{32}x^{-\frac{6}{5}}dx
derivative of e^{x^{-1}}
\frac{d}{dx}(e^{x^{-1}})
derivative of 3x(6x-5x^2)
\frac{d}{dx}(3x(6x-5x^{2}))
derivative of (80e^{-x/(10})-40x)
\frac{d}{dx}((80e^{-\frac{x}{10}})-40x)
area x^2-2x,3x+6
area\:x^{2}-2x,3x+6
limit as x approaches 3 of-3
\lim\:_{x\to\:3}(-3)
derivative of y=((x^2+2)/(x^2-2))^6
derivative\:y=(\frac{x^{2}+2}{x^{2}-2})^{6}
(\partial)/(\partial x)(xln(z^3+x^6))
\frac{\partial\:}{\partial\:x}(x\ln(z^{3}+x^{6}))
derivative of y=tan(pi-9/x)
derivative\:y=\tan(π-\frac{9}{x})
derivative of 12+2.8sin((2pi)/(365)(t-80))
derivative\:12+2.8\sin(\frac{2π}{365}(t-80))
sum from n=0 to infinity of 4/(2^n)
\sum\:_{n=0}^{\infty\:}\frac{4}{2^{n}}
f(x)=sqrt(cos(x))
f(x)=\sqrt{\cos(x)}
slope of (-18-20)(-18-15)
slope\:(-18-20)(-18-15)
integral of ((x^6-5x)/(x^2))
\int\:(\frac{x^{6}-5x}{x^{2}})dx
limit as x approaches 0 of x/(sin(x/2))
\lim\:_{x\to\:0}(\frac{x}{\sin(\frac{x}{2})})
derivative of (-3x^4-5x^3+2/(-5x^4))
\frac{d}{dx}(\frac{-3x^{4}-5x^{3}+2}{-5x^{4}})
(\partial)/(\partial x)(1/(1+x))
\frac{\partial\:}{\partial\:x}(\frac{1}{1+x})
(\partial)/(\partial x)(x^2-2x^2y-5xy^2)
\frac{\partial\:}{\partial\:x}(x^{2}-2x^{2}y-5xy^{2})
integral of (2x)^2(5+3^4)^{1/4}
\int\:(2x)^{2}(5+3^{4})^{\frac{1}{4}}dx
(d^2)/(dx^2)(\sqrt[7]{x})
\frac{d^{2}}{dx^{2}}(\sqrt[7]{x})
derivative of tan(2x+5)
derivative\:\tan(2x+5)
integral of 2+tan^2(x)
\int\:2+\tan^{2}(x)dx
limit as x approaches infinity+of 6x
\lim\:_{x\to\:\infty\:+}(6x)
7x^2y^{''}+15xy^'+y=48x+7
7x^{2}y^{\prime\:\prime\:}+15xy^{\prime\:}+y=48x+7
derivative of 3/4 x^{4/3}-3/8 x^{2/3}+6
derivative\:\frac{3}{4}x^{\frac{4}{3}}-\frac{3}{8}x^{\frac{2}{3}}+6
integral of sin(2x)-4e^{3x}
\int\:\sin(2x)-4e^{3x}dx
sum from n=2 to infinity of 1/(n^2+4n)
\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}+4n}
limit as x approaches 1 of (x^2-1)^{x^2}
\lim\:_{x\to\:1}((x^{2}-1)^{x^{2}})
y^'=(xy)/2
y^{\prime\:}=\frac{xy}{2}
integral from 0 to 1 of x^4e^{5x}
\int\:_{0}^{1}x^{4}e^{5x}dx
integral of atan^2(θ)
\int\:a\tan^{2}(θ)dθ
derivative of 4sqrt(x)+ln(x+1)
\frac{d}{dx}(4\sqrt{x}+\ln(x+1))
(dy}{dx}=\frac{6xsec(y/x)+y)/x
\frac{dy}{dx}=\frac{6x\sec(\frac{y}{x})+y}{x}
limit as x approaches 0+of (tan(3x))x
\lim\:_{x\to\:0+}((\tan(3x))x)
tangent of x^2-4x+25
tangent\:x^{2}-4x+25
(\partial}{\partial x}(830x-\frac{25000)/x-(5400)/y+2280y+457950)
\frac{\partial\:}{\partial\:x}(830x-\frac{25000}{x}-\frac{5400}{y}+2280y+457950)
(\partial)/(\partial x)(e^xcos(y)-z)
\frac{\partial\:}{\partial\:x}(e^{x}\cos(y)-z)
integral of (x^3+1)/(x^3-x^2)
\int\:\frac{x^{3}+1}{x^{3}-x^{2}}dx
d/(dy)(ln(y^2))
\frac{d}{dy}(\ln(y^{2}))
integral of ((x^3+7)/(x^2))
\int\:(\frac{x^{3}+7}{x^{2}})dx
integral from-3 to 0 of |x+2|
\int\:_{-3}^{0}\left|x+2\right|dx
derivative of 1/(arcsin(x))
\frac{d}{dx}(\frac{1}{\arcsin(x)})
(\partial)/(\partial x)(x/((x+y)))
\frac{\partial\:}{\partial\:x}(\frac{x}{(x+y)})
integral of x/(sqrt(4x-x^2))
\int\:\frac{x}{\sqrt{4x-x^{2}}}dx
integral of 2x(x^2+1)^8
\int\:2x(x^{2}+1)^{8}dx
simplify (g(x))^3
simplify\:(g(x))^{3}
limit as x approaches 0 of x^3e^{-x^2}
\lim\:_{x\to\:0}(x^{3}e^{-x^{2}})
integral from 1/2 to 5 of 1/((2x-1)^{1/3)}
\int\:_{\frac{1}{2}}^{5}\frac{1}{(2x-1)^{\frac{1}{3}}}dx
integral of 12sin^2(xco)s^2x
\int\:12\sin^{2}(xco)s^{2}xdx
integral of (x^{1/3}-2x^{-2/3}+3)
\int\:(x^{\frac{1}{3}}-2x^{-\frac{2}{3}}+3)dx
integral of (1/x+2/(x^2)+3/(x^3))
\int\:(\frac{1}{x}+\frac{2}{x^{2}}+\frac{3}{x^{3}})dx
integral of 7/x
\int\:\frac{7}{x}dx
y(1+xy)dx+(2y-x)dy=0
y(1+xy)dx+(2y-x)dy=0
integral of (2/x)
\int\:(\frac{2}{x})dx
tangent of f(x)=6x^3-6x^2+4
tangent\:f(x)=6x^{3}-6x^{2}+4
limit as x approaches 0+of 2x^{sin(3x)}
\lim\:_{x\to\:0+}(2x^{\sin(3x)})
integral of xe^{5x+pi}
\int\:xe^{5x+π}dx
limit as x approaches-8 of-(3x)/(x+8)
\lim\:_{x\to\:-8}(-\frac{3x}{x+8})
derivative of 3x^3sqrt(25-x^2)
derivative\:3x^{3}\sqrt{25-x^{2}}
integral from 6 to 8 of (70)/((x-6)^3)
\int\:_{6}^{8}\frac{70}{(x-6)^{3}}dx
taylor sqrt(1-3x^2)
taylor\:\sqrt{1-3x^{2}}
f^'(x)=f(x)(1-f(x))
f^{\prime\:}(x)=f(x)(1-f(x))
integral of ((7sin(x)+4sec(x)))/(tan(x))
\int\:\frac{(7\sin(x)+4\sec(x))}{\tan(x)}dx
derivative of f(x)=200+7/x+(x^2)/7
derivative\:f(x)=200+\frac{7}{x}+\frac{x^{2}}{7}
y^'=x(9-y)
y^{\prime\:}=x(9-y)
sum from n=1 to infinity of 1/(n+9)
\sum\:_{n=1}^{\infty\:}\frac{1}{n+9}
integral of ((x-4)^2(x+1))/x
\int\:\frac{(x-4)^{2}(x+1)}{x}dx
xy^'=2y+8x
xy^{\prime\:}=2y+8x
integral from 2 to 3 of (x^2+1)/(x^3+3x)
\int\:_{2}^{3}\frac{x^{2}+1}{x^{3}+3x}dx
integral from 0 to 5 of x/(x-2)
\int\:_{0}^{5}\frac{x}{x-2}dx
integral of 3xsec^2(4)x^2
\int\:3x\sec^{2}(4)x^{2}dx
(dx)/(dt)=rx
\frac{dx}{dt}=rx
derivative of-cos(piy)dx
derivative\:-\cos(πy)dx
integral of (3x^2-1)e^{x^3-x}
\int\:(3x^{2}-1)e^{x^{3}-x}dx
derivative of sqrt(35x)ln(10x)
derivative\:\sqrt{35x}\ln(10x)
(1+x^4)dy+x(1+4y^2)dx=0,y(1)=0
(1+x^{4})dy+x(1+4y^{2})dx=0,y(1)=0
4y^{''}-y=1
4y^{\prime\:\prime\:}-y=1
integral of sqrt(e^{3x)}
\int\:\sqrt{e^{3x}}dx
tangent of (x^2-9)^2
tangent\:(x^{2}-9)^{2}
y^{''}-3y^'-10y=4,y(0)=0,y^'(0)=0
y^{\prime\:\prime\:}-3y^{\prime\:}-10y=4,y(0)=0,y^{\prime\:}(0)=0
integral from 1 to e^7 of (ln^2(x^2))/x
\int\:_{1}^{e^{7}}\frac{\ln^{2}(x^{2})}{x}dx
sum from n=1 to infinity of (3/n)^4
\sum\:_{n=1}^{\infty\:}(\frac{3}{n})^{4}
integral of 1/(sin^2(t))
\int\:\frac{1}{\sin^{2}(t)}dt
derivative of r=10^{2sqrt(t)}
derivative\:r=10^{2\sqrt{t}}
(\partial)/(\partial x)(sin(pi(4x-3y)))
\frac{\partial\:}{\partial\:x}(\sin(π(4x-3y)))
sum from n=1 to infinity}((\sqrt{n of))/(ln(n))
\sum\:_{n=1}^{\infty\:}\frac{(\sqrt{n})}{\ln(n)}
(\partial)/(\partial x)(x+y+ln(xy))
\frac{\partial\:}{\partial\:x}(x+y+\ln(xy))
integral of sqrt(1-\sqrt{v)}
\int\:\sqrt{1-\sqrt{v}}dv
integral of cot(1)
\int\:\cot(1)dx
(\partial)/(\partial x)(log_{e}(x^2+y^4))
\frac{\partial\:}{\partial\:x}(\log_{e}(x^{2}+y^{4}))
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