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Popular Calculus Problems
integral from 0 to 1 of sqrt(x^2+1)
\int\:_{0}^{1}\sqrt{x^{2}+1}dx
(\partial)/(\partial y)(cos(x+y^2))
\frac{\partial\:}{\partial\:y}(\cos(x+y^{2}))
(\partial)/(\partial x)(2ye^{4x})
\frac{\partial\:}{\partial\:x}(2ye^{4x})
integral of (80-3t-(2t+30))
\int\:(80-3t-(2t+30))dt
derivative of (x-x^2/(2-3x+x^2))
\frac{d}{dx}(\frac{x-x^{2}}{2-3x+x^{2}})
integral from 0 to ln(6) of e^x-e^{-3x}
\int\:_{0}^{\ln(6)}e^{x}-e^{-3x}dx
derivative of y=(4x)/(9-tan(x))
derivative\:y=\frac{4x}{9-\tan(x)}
derivative of arctan(x)
derivative\:\arctan(x)
integral from 0 to 1 of (xsqrt(2-x^2))
\int\:_{0}^{1}(x\sqrt{2-x^{2}})dx
tangent of y= x/((1+x^2),\at (3,0.3))
tangent\:y=\frac{x}{(1+x^{2}),\at\:(3,0.3)}
derivative of sqrt(1+4sin(x))
\frac{d}{dx}(\sqrt{1+4\sin(x)})
integral of-2ysqrt(-y^2+2)
\int\:-2y\sqrt{-y^{2}+2}dy
tangent of f(x)=1-7x^2,(-2,-27)
tangent\:f(x)=1-7x^{2},(-2,-27)
(\partial)/(\partial x)(e^{xy}+x/y)
\frac{\partial\:}{\partial\:x}(e^{xy}+\frac{x}{y})
y^{''}+13y^'+42y=0
y^{\prime\:\prime\:}+13y^{\prime\:}+42y=0
y^{''}+4y=0,y(0)=0,y^'(0)=0
y^{\prime\:\prime\:}+4y=0,y(0)=0,y^{\prime\:}(0)=0
integral of (x^6)/6
\int\:\frac{x^{6}}{6}dx
integral from 2 to 8 of x
\int\:_{2}^{8}xdx
integral of cos^3(xsi)n^4x
\int\:\cos^{3}(xsi)n^{4}xdx
integral of (x^3)/(324)
\int\:\frac{x^{3}}{324}dx
integral from 0 to infinity of x/(1+x^3)
\int\:_{0}^{\infty\:}\frac{x}{1+x^{3}}dx
limit as x approaches 4 of x^2
\lim\:_{x\to\:4}(x^{2})
9y^{''}+4y=0
9y^{\prime\:\prime\:}+4y=0
y^{''}+4y=x^2+3e^x,y(0)=0,y^'(0)=2
y^{\prime\:\prime\:}+4y=x^{2}+3e^{x},y(0)=0,y^{\prime\:}(0)=2
derivative of sqrt(2-4x)
derivative\:\sqrt{2-4x}
integral of 9sin(sqrt(x))
\int\:9\sin(\sqrt{x})dx
integral from 0 to 2 of 2pix(x^2)
\int\:_{0}^{2}2πx(x^{2})dx
derivative of e^{x*cos(x})
\frac{d}{dx}(e^{x\cdot\:\cos(x)})
integral from 0 to 6 of pi(2x)^2
\int\:_{0}^{6}π(2x)^{2}dx
derivative of ln(sqrt((x^2/(x+1))))
\frac{d}{dx}(\ln(\sqrt{\frac{x^{2}}{x+1}}))
integral of ((cos(x)))/(((sin^2(x))^{1/3))}
\int\:\frac{(\cos(x))}{((\sin^{2}(x))^{\frac{1}{3}})}dx
d/(dt)(t^2+4t)
\frac{d}{dt}(t^{2}+4t)
y^'+10y=1
y^{\prime\:}+10y=1
limit as x approaches 0 of 2+(3/x)
\lim\:_{x\to\:0}(2+(\frac{3}{x}))
(\partial)/(\partial y)(xy+1/x+1/y)
\frac{\partial\:}{\partial\:y}(xy+\frac{1}{x}+\frac{1}{y})
integral of tan^3(10x)
\int\:\tan^{3}(10x)dx
integral of (5x-3)/(x^2-2x-3)
\int\:\frac{5x-3}{x^{2}-2x-3}dx
(\partial)/(\partial x)((x+y)/(x-y))
\frac{\partial\:}{\partial\:x}(\frac{x+y}{x-y})
derivative of sin(cos(4x))
\frac{d}{dx}(\sin(\cos(4x)))
derivative of 1/(5x^{4/5)}
derivative\:\frac{1}{5x^{\frac{4}{5}}}
derivative of f(x)=(x^3+1)/(x^3-1)
derivative\:f(x)=\frac{x^{3}+1}{x^{3}-1}
x^3y^{'''}+xy^'-y=0
x^{3}y^{\prime\:\prime\:\prime\:}+xy^{\prime\:}-y=0
integral of e^{-1}
\int\:e^{-1}
derivative of f(x)=(2ln(x))/x
derivative\:f(x)=\frac{2\ln(x)}{x}
(\partial)/(\partial x)(2x(4+y)^{-1})
\frac{\partial\:}{\partial\:x}(2x(4+y)^{-1})
derivative of-2(e^xsin(x+cos(x)e^x))
\frac{d}{dx}(-2(e^{x}\sin(x)+\cos(x)e^{x}))
integral of 1/(5+2x^4)(8x^3)
\int\:\frac{1}{5+2x^{4}}(8x^{3})dx
derivative of 8sin(x-4sqrt(2x))
\frac{d}{dx}(8\sin(x)-4\sqrt{2x})
derivative of 1/(\sqrt[5]{x^2})
\frac{d}{dx}(\frac{1}{\sqrt[5]{x^{2}}})
laplacetransform {cos(t)}
laplacetransform\:\left\{\cos(t)\right\}
f(t)=cos(8t)
f(t)=\cos(8t)
derivative of f(x)=x^3-3x+4
derivative\:f(x)=x^{3}-3x+4
y^{''}+6y^'+5y=2x
y^{\prime\:\prime\:}+6y^{\prime\:}+5y=2x
tangent of f(x)=3x^{1/2}+x^{3/2},\at x=16
tangent\:f(x)=3x^{\frac{1}{2}}+x^{\frac{3}{2}},\at\:x=16
integral of 2/(x(ln(x))^2)
\int\:\frac{2}{x(\ln(x))^{2}}dx
derivative of (x^2)/((2+x))
derivative\:\frac{x^{2}}{(2+x)}
y^{''}-8y^'-17y=0
y^{\prime\:\prime\:}-8y^{\prime\:}-17y=0
derivative of 3x^2y-2x^2y^2+3y
\frac{d}{dx}(3x^{2}y-2x^{2}y^{2}+3y)
integral from 0 to pi/4 of 2tan^5(x)
\int\:_{0}^{\frac{π}{4}}2\tan^{5}(x)dx
taylor x^2-2x+42
taylor\:x^{2}-2x+42
area sqrt(1/7 x),7x^2
area\:\sqrt{\frac{1}{7}x},7x^{2}
limit as x approaches infinity of (x^2-1)e^{-x^2}
\lim\:_{x\to\:\infty\:}((x^{2}-1)e^{-x^{2}})
integral of-xcos(x+pi/3)
\int\:-x\cos(x+\frac{π}{3})dx
integral of (2sqrt(x)-3\sqrt[4]{x})
\int\:(2\sqrt{x}-3\sqrt[4]{x})dx
integral of x^2e^{-2x^3}
\int\:x^{2}e^{-2x^{3}}dx
integral of sqrt(2[1-cos^2(\sqrt{2x))]}
\int\:\sqrt{2[1-\cos^{2}(\sqrt{2x})]}dx
integral from-1 to 1 of pi(2-2x^2)^2
\int\:_{-1}^{1}π(2-2x^{2})^{2}dx
y^{''}+2y^'-15y=4e^{-t}
y^{\prime\:\prime\:}+2y^{\prime\:}-15y=4e^{-t}
(\partial)/(\partial y)(x^2-y)
\frac{\partial\:}{\partial\:y}(x^{2}-y)
2y^{''}+5y^'-3y=0
2y^{\prime\:\prime\:}+5y^{\prime\:}-3y=0
(\partial)/(\partial y)(2xy+z^2)
\frac{\partial\:}{\partial\:y}(2xy+z^{2})
(\partial)/(\partial x)(3xln(y)+yln(z)-2x)
\frac{\partial\:}{\partial\:x}(3x\ln(y)+y\ln(z)-2x)
integral of sqrt(x)(x+1/x)
\int\:\sqrt{x}(x+\frac{1}{x})dx
integral of x^2
\int\:x^{2}dx
limit as x approaches 0+of (2x)/(|x|)
\lim\:_{x\to\:0+}(\frac{2x}{\left|x\right|})
derivative of sqrt(x)(x^2-1)
\frac{d}{dx}(\sqrt{x}(x^{2}-1))
derivative of sqrt((x+2^2*(x^2)/2))
\frac{d}{dx}(\sqrt{(x+2)^{2}\cdot\:\frac{x^{2}}{2}})
derivative of (e^x/(5x^3))
\frac{d}{dx}(\frac{e^{x}}{5x^{3}})
tangent of f(x)=(1+5x)^{12},(0,1)
tangent\:f(x)=(1+5x)^{12},(0,1)
10y^'=10*9.81-5y
10y^{\prime\:}=10\cdot\:9.81-5y
tangent of y= 1/(x-1),\at x=6
tangent\:y=\frac{1}{x-1},\at\:x=6
y^{''}-4y^'+3y=0
y^{\prime\:\prime\:}-4y^{\prime\:}+3y=0
derivative of-10sin(2x+10)
\frac{d}{dx}(-10\sin(2x+10))
y^{''}+25y=-20sin(5t)
y^{\prime\:\prime\:}+25y=-20\sin(5t)
derivative of 3cos(3x+1)
\frac{d}{dx}(3\cos(3x+1))
limit as x approaches 81 of ((\sqrt[4]{x}-3))/(x-81)
\lim\:_{x\to\:81}(\frac{(\sqrt[4]{x}-3)}{x-81})
(\partial)/(\partial u)(b((((Nu))/(V(u)))^{(2/3)}))
\frac{\partial\:}{\partial\:u}(b((\frac{(Nu)}{V(u)})^{(\frac{2}{3})}))
integral from 1 to infinity of 1/(x^2)
\int\:_{1}^{\infty\:}\frac{1}{x^{2}}dx
taylor ln(x+1),2
taylor\:\ln(x+1),2
(\partial)/(\partial x)((x^2)/((y-x)^2))
\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{(y-x)^{2}})
sum from n=1 to infinity of 2/(n^8)
\sum\:_{n=1}^{\infty\:}\frac{2}{n^{8}}
integral of 8x^4
\int\:8x^{4}dx
integral of sqrt(x)sin^2(x^{3/2}-1)
\int\:\sqrt{x}\sin^{2}(x^{\frac{3}{2}}-1)dx
derivative of 7x^3-3x^2+3x-12
\frac{d}{dx}(7x^{3}-3x^{2}+3x-12)
f(x)=(ln(x+1))^2
f(x)=(\ln(x+1))^{2}
derivative of (x^2/(1+x^2))
\frac{d}{dx}(\frac{x^{2}}{1+x^{2}})
integral of (2x^3)/(x^4+5)
\int\:\frac{2x^{3}}{x^{4}+5}dx
derivative of acos^2(x)+bx
derivative\:a\cos^{2}(x)+bx
integral of (sin(x)-4cos(x))
\int\:(\sin(x)-4\cos(x))dx
integral of (x+3)/((x-1)(x^2+1))
\int\:\frac{x+3}{(x-1)(x^{2}+1)}dx
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