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Popular Calculus Problems
ty^'+yt=1-y
ty^{\prime\:}+yt=1-y
integral from 0 to pi of sec^2(x/4)
\int\:_{0}^{π}\sec^{2}(\frac{x}{4})dx
(\partial)/(\partial x)(sqrt(x^2+8xy+3y^2))
\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+8xy+3y^{2}})
derivative of (x^2)/(x-5)
derivative\:\frac{x^{2}}{x-5}
limit as n approaches infinity of n+1
\lim\:_{n\to\:\infty\:}(n+1)
integral of (x^2)/(x^2+3)
\int\:\frac{x^{2}}{x^{2}+3}dx
(\partial)/(\partial x)(4x-y^2-4)
\frac{\partial\:}{\partial\:x}(4x-y^{2}-4)
integral of e^{-x}*sin(x)
\int\:e^{-x}\cdot\:\sin(x)dx
integral of 9tan^3(θ)
\int\:9\tan^{3}(θ)dθ
limit as x approaches 2 of 4x^2+5x+3
\lim\:_{x\to\:2}(4x^{2}+5x+3)
integral of 1/(xsqrt(6+4x))
\int\:\frac{1}{x\sqrt{6+4x}}dx
derivative of f(x)=x^2(2x+9)^3
derivative\:f(x)=x^{2}(2x+9)^{3}
integral from 0 to pi of cos(4x)
\int\:_{0}^{π}\cos(4x)dx
(dh)/(dt)+8*h=4
\frac{dh}{dt}+8\cdot\:h=4
(dy)/(dx)=6-y
\frac{dy}{dx}=6-y
integral of (4e^x)
\int\:(4e^{x})dx
derivative of ((sec(9x+1))/((x^3e^{(-x)))})
\frac{d}{dx}(\frac{(\sec(9x)+1)}{(x^{3}e^{(-x)})})
integral of 3cos(pi-t)+(pi-t)^2
\int\:3\cos(π-t)+(π-t)^{2}dt
integral of 4/((1+t^2))
\int\:\frac{4}{(1+t^{2})}dt
integral of 5/(t+1)
\int\:\frac{5}{t+1}dt
integral of 1/(sqrt(16-25x^2))
\int\:\frac{1}{\sqrt{16-25x^{2}}}dx
derivative of 5/x-2/(x^3)+1/(x^4)
derivative\:\frac{5}{x}-\frac{2}{x^{3}}+\frac{1}{x^{4}}
integral of (4x^2+8x+9)^6(x+1)
\int\:(4x^{2}+8x+9)^{6}(x+1)dx
derivative of arccos(x)
derivative\:\arccos(x)
limit as x approaches 0 of (e^x)/(x^2)
\lim\:_{x\to\:0}(\frac{e^{x}}{x^{2}})
(d^4)/(dx^4)(x^{-2})
\frac{d^{4}}{dx^{4}}(x^{-2})
tangent of y=x^2-3x
tangent\:y=x^{2}-3x
integral from 0 to 1 of sin(pix+pi/4)
\int\:_{0}^{1}\sin(πx+\frac{π}{4})dx
integral of cos(2x)sqrt(sin(2x))
\int\:\cos(2x)\sqrt{\sin(2x)}dx
derivative of sec(ln(x))
\frac{d}{dx}(\sec(\ln(x)))
integral of e^{2t}sin(t)
\int\:e^{2t}\sin(t)dt
derivative of a^6+cos^6(x)
derivative\:a^{6}+\cos^{6}(x)
integral from-3 to 1 of (1+4x)
\int\:_{-3}^{1}(1+4x)dx
limit as x approaches 6 of sqrt(2x-5)
\lim\:_{x\to\:6}(\sqrt{2x-5})
limit as x approaches 2 of f(x)x
\lim\:_{x\to\:2}(f(x)x)
(\partial)/(\partial θ)(sin^2(θ))
\frac{\partial\:}{\partial\:θ}(\sin^{2}(θ))
d/(d{r)}(({r}-s+cos({r}+s)+sin({r}+s))^2)
\frac{d}{d{r}}(({r}-s+\cos({r}+s)+\sin({r}+s))^{2})
(dx)/(dt)=3sqrt(xt)
\frac{dx}{dt}=3\sqrt{xt}
limit as x approaches 1 of 3x^2+2x
\lim\:_{x\to\:1}(3x^{2}+2x)
integral from pi/2 to pi of 4cot(x/3)
\int\:_{\frac{π}{2}}^{π}4\cot(\frac{x}{3})dx
sum from n=0 to infinity of n/((2n+1)!)
\sum\:_{n=0}^{\infty\:}\frac{n}{(2n+1)!}
tangent of f(x)=9x^2-x^3,\at x=2
tangent\:f(x)=9x^{2}-x^{3},\at\:x=2
integral of e^2sin(x)
\int\:e^{2}\sin(x)dx
integral from 0 to 3 of 3x-1
\int\:_{0}^{3}3x-1dx
y^{''}-9y^'+2y=xe^x
y^{\prime\:\prime\:}-9y^{\prime\:}+2y=xe^{x}
integral of (x+2)/(sqrt(4x-x^2))
\int\:\frac{x+2}{\sqrt{4x-x^{2}}}dx
derivative of 2/((x+1^3))
\frac{d}{dx}(\frac{2}{(x+1)^{3}})
integral of ((x^2)-3x^2)/(x^1)
\int\:\frac{(x^{2})-3x^{2}}{x^{1}}dx
derivative of f(1)=(x^3+2x+8)^3
derivative\:f(1)=(x^{3}+2x+8)^{3}
tangent of (x^2)/(x-3)
tangent\:\frac{x^{2}}{x-3}
integral of ln(x-20)
\int\:\ln(x-20)dx
derivative of 1+sqrt(t)
derivative\:1+\sqrt{t}
limit as x approaches 0+of x^{2*sqrt(x)}
\lim\:_{x\to\:0+}(x^{2\cdot\:\sqrt{x}})
integral from 1 to infinity of 1/(sqrt(x)+x\sqrt{x)}
\int\:_{1}^{\infty\:}\frac{1}{\sqrt{x}+x\sqrt{x}}dx
derivative of ln((e^x+1)/(e^x-1))
derivative\:\ln(\frac{e^{x}+1}{e^{x}-1})
integral from 1 to 2 of 1/((3-5x)^2)
\int\:_{1}^{2}\frac{1}{(3-5x)^{2}}dx
derivative of pi^{x^2}
derivative\:π^{x^{2}}
integral of 1/(5-4x)
\int\:\frac{1}{5-4x}dx
(\partial)/(\partial b)(a/b)
\frac{\partial\:}{\partial\:b}(\frac{a}{b})
integral of (7-98x)/(sqrt(16-49x^2))
\int\:\frac{7-98x}{\sqrt{16-49x^{2}}}dx
integral of (2x+8)/((x+3)^2)
\int\:\frac{2x+8}{(x+3)^{2}}dx
integral of 9/(sqrt(x^2+16))
\int\:\frac{9}{\sqrt{x^{2}+16}}dx
integral of t^{24}e^{-t^{25}}
\int\:t^{24}e^{-t^{25}}dt
limit as x approaches 0 of (x)^{3x}
\lim\:_{x\to\:0}((x)^{3x})
integral of (x^3+x+1)/(x(x^2+1))
\int\:\frac{x^{3}+x+1}{x(x^{2}+1)}dx
area y=9x,y=x^2-10
area\:y=9x,y=x^{2}-10
tangent of x^4,\at x=-1/3
tangent\:x^{4},\at\:x=-\frac{1}{3}
integral from 0 to 1 of 3e^{-3t}
\int\:_{0}^{1}3e^{-3t}dt
(\partial)/(\partial x)(log_{13}(1+x^2))
\frac{\partial\:}{\partial\:x}(\log_{13}(1+x^{2}))
derivative of (3x+1^{1/2})
\frac{d}{dx}((3x+1)^{\frac{1}{2}})
derivative of (x^2-3x+2(2x^3+1))
\frac{d}{dx}((x^{2}-3x+2)(2x^{3}+1))
derivative of cos((pix^8))
\frac{d}{dx}(\cos((πx)^{8}))
integral of 8sin^6(x)cos(x)
\int\:8\sin^{6}(x)\cos(x)dx
derivative of y=arctan(cos(x))
derivative\:y=\arctan(\cos(x))
derivative of e^{2x}+x^3
\frac{d}{dx}(e^{2x}+x^{3})
(\partial)/(\partial y)(2x^3y+cos(x^2))
\frac{\partial\:}{\partial\:y}(2x^{3}y+\cos(x^{2}))
derivative of Ce^{3x}
\frac{d}{dx}(Ce^{3x})
integral of 1/((x-1)(x-3)(x+4))
\int\:\frac{1}{(x-1)(x-3)(x+4)}dx
(sqrt(9-x^2))^'
(\sqrt{9-x^{2}})^{\prime\:}
f(x)=xe^{x^2}
f(x)=xe^{x^{2}}
derivative of 240(1-3/(3+e^{-0.5x}))
\frac{d}{dx}(240(1-\frac{3}{3+e^{-0.5x}}))
laplacetransform e^{3/2}
laplacetransform\:e^{\frac{3}{2}}
integral of x^3sqrt(3+x^4)
\int\:x^{3}\sqrt{3+x^{4}}dx
derivative of 5sin(9x)
\frac{d}{dx}(5\sin(9x))
integral from b to 1 of 6ln(x)
\int\:_{b}^{1}6\ln(x)dx
(\partial)/(\partial x)(sqrt(x+\sqrt{x)})
\frac{\partial\:}{\partial\:x}(\sqrt{x+\sqrt{x}})
integral of 1/((x-4)^2)
\int\:\frac{1}{(x-4)^{2}}dx
derivative of sin(2x+cos^2(x))
\frac{d}{dx}(\sin(2x)+\cos^{2}(x))
derivative of 4ln(5x)
\frac{d}{dx}(4\ln(5x))
derivative of (x-4e^{3x})
\frac{d}{dx}((x-4)e^{3x})
derivative of e^{-2x}
derivative\:e^{-2x}
limit as x approaches 0 of coth(x)
\lim\:_{x\to\:0}(\coth(x))
derivative of 3x^2+4
derivative\:3x^{2}+4
derivative of 1/(1-x)
derivative\:\frac{1}{1-x}
derivative of (2x^3/(sqrt(x^2-3)))
\frac{d}{dx}(\frac{2x^{3}}{\sqrt{x^{2}-3}})
limit as x approaches 0 of (cot(2x))/(csc(x))
\lim\:_{x\to\:0}(\frac{\cot(2x)}{\csc(x)})
tangent of f(x)=x^2+8,\at x=1
tangent\:f(x)=x^{2}+8,\at\:x=1
tangent of f(x)=x^2+3,\at x=-3
tangent\:f(x)=x^{2}+3,\at\:x=-3
derivative of (e^x+1)^2
derivative\:(e^{x}+1)^{2}
limit as x approaches 0 of (x^2+3)/(x^4)
\lim\:_{x\to\:0}(\frac{x^{2}+3}{x^{4}})
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