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Popular Calculus Problems
limit as x approaches-1 of x^2+4x
\lim\:_{x\to\:-1}(x^{2}+4x)
(dy)/(dt)=4y+y^4
\frac{dy}{dt}=4y+y^{4}
tangent of f(x)=-(4x)/(x^2+1),\at x=0
tangent\:f(x)=-\frac{4x}{x^{2}+1},\at\:x=0
integral of r^2((r^3)/(15)-8)^4
\int\:r^{2}(\frac{r^{3}}{15}-8)^{4}dr
(\partial)/(\partial x)((s^2+4)/(t-3))
\frac{\partial\:}{\partial\:x}(\frac{s^{2}+4}{t-3})
derivative of ln(arctan(2x^5))
\frac{d}{dx}(\ln(\arctan(2x^{5})))
integral of 1/(6x^5)
\int\:\frac{1}{6x^{5}}dx
derivative of 3*2^{2x+1}
derivative\:3\cdot\:2^{2x+1}
integral from 0 to 1 of rsqrt(1-r^2)
\int\:_{0}^{1}r\sqrt{1-r^{2}}dr
integral of ((x^3)/(x-1))
\int\:(\frac{x^{3}}{x-1})dx
derivative of (1-x^3-3x(1-x)^2)
\frac{d}{dx}((1-x)^{3}-3x(1-x)^{2})
(dy)/(dx)=(x-1)/(3x^2-6x-1)
\frac{dy}{dx}=\frac{x-1}{3x^{2}-6x-1}
integral of (ln(x))2
\int\:(\ln(x))2dx
derivative of (ln(x))/(ln(2))
derivative\:\frac{\ln(x)}{\ln(2)}
integral of (sqrt(4x^2+9))/(x^4)
\int\:\frac{\sqrt{4x^{2}+9}}{x^{4}}dx
integral of x/(sqrt(9+x^4))
\int\:\frac{x}{\sqrt{9+x^{4}}}dx
taylor (1+0.5x)/(1-0.5x)
taylor\:\frac{1+0.5x}{1-0.5x}
derivative of (3x/(2x^2+1))
\frac{d}{dx}(\frac{3x}{2x^{2}+1})
(\partial)/(\partial x)(1/2 (x^2+6y^2))
\frac{\partial\:}{\partial\:x}(\frac{1}{2}(x^{2}+6y^{2}))
tangent of f(x)=x(x^2-4x+5)^4,\at x=2
tangent\:f(x)=x(x^{2}-4x+5)^{4},\at\:x=2
inverse oflaplace 1/(s^2+2s-3)
inverselaplace\:\frac{1}{s^{2}+2s-3}
integral of (e^{-st})/s
\int\:\frac{e^{-st}}{s}dt
integral of ln(6x+1)
\int\:\ln(6x+1)dx
derivative of sin(e^x-1)
\frac{d}{dx}(\sin(e^{x}-1))
tangent of 4x^3-4x^2+3
tangent\:4x^{3}-4x^{2}+3
sum from n=1 to infinity of (n^3)/(e^n)
\sum\:_{n=1}^{\infty\:}\frac{n^{3}}{e^{n}}
limit as x approaches 1+of x^{8/(1-x)}
\lim\:_{x\to\:1+}(x^{\frac{8}{1-x}})
limit as x approaches 0-of |x|
\lim\:_{x\to\:0-}(\left|x\right|)
(\partial)/(\partial y)(e^{3x}sin(3y))
\frac{\partial\:}{\partial\:y}(e^{3x}\sin(3y))
tangent of f(x)=(-2x)/(x^2+1)
tangent\:f(x)=\frac{-2x}{x^{2}+1}
sum from n=1 to infinity of (2n+1)/(4^n)
\sum\:_{n=1}^{\infty\:}\frac{2n+1}{4^{n}}
integral from 0 to sqrt(7 of)(x^3)/(\sqrt[3]{1+x^2)}
\int\:_{0}^{\sqrt{7}}\frac{x^{3}}{\sqrt[3]{1+x^{2}}}dx
limit as x approaches 3 of ((-4)(0))/4
\lim\:_{x\to\:3}(\frac{(-4)(0)}{4})
derivative of (x^7+2)/(x^7)
derivative\:\frac{x^{7}+2}{x^{7}}
tangent of 11-x^2(3.2)
tangent\:11-x^{2}(3.2)
integral of tan^4(6x)sec^2(6x)
\int\:\tan^{4}(6x)\sec^{2}(6x)dx
(\partial)/(\partial y)(sqrt(y^2-9))
\frac{\partial\:}{\partial\:y}(\sqrt{y^{2}-9})
(dy)/(dx)=-(4x+4y)/(4x+9y)
\frac{dy}{dx}=-\frac{4x+4y}{4x+9y}
limit as x approaches 2+of (x-3)/(x^2-4)
\lim\:_{x\to\:2+}(\frac{x-3}{x^{2}-4})
(\partial)/(\partial y)(x^4+8xy^7)
\frac{\partial\:}{\partial\:y}(x^{4}+8xy^{7})
integral of (ln|x|)/x
\int\:\frac{\ln\left|x\right|}{x}dx
derivative of f(t)=(3t-1)^4(2t+1)^{-3}
derivative\:f(t)=(3t-1)^{4}(2t+1)^{-3}
limit as x approaches 0 of (tan(kx))/x
\lim\:_{x\to\:0}(\frac{\tan(kx)}{x})
integral of z^3e^z
\int\:z^{3}e^{z}dz
derivative of arctan(ln(x^2))
\frac{d}{dx}(\arctan(\ln(x^{2})))
derivative of ln(sqrt(2x))
\frac{d}{dx}(\ln(\sqrt{2x}))
integral of 8/(x+1)
\int\:\frac{8}{x+1}dx
(\partial)/(\partial x)(5/(5x+3y))
\frac{\partial\:}{\partial\:x}(\frac{5}{5x+3y})
inverse oflaplace (10)/(s(s+2)(s+3)^2)
inverselaplace\:\frac{10}{s(s+2)(s+3)^{2}}
limit as x approaches 0-of xsin(1/x)
\lim\:_{x\to\:0-}(x\sin(\frac{1}{x}))
xy^'+y=-5xy^2,y(1)=7
xy^{\prime\:}+y=-5xy^{2},y(1)=7
integral of arccot(2y)
\int\:\arccot(2y)dy
y^'=(xy^3)/(16)
y^{\prime\:}=\frac{xy^{3}}{16}
integral of x^2(4-2x^2)
\int\:x^{2}(4-2x^{2})dx
derivative of f(x)=sqrt(x)(x^3-x)
derivative\:f(x)=\sqrt{x}(x^{3}-x)
derivative of (6x-3/(5x+8))
\frac{d}{dx}(\frac{6x-3}{5x+8})
integral of (4x-11)/(2x^2-11x+15)
\int\:\frac{4x-11}{2x^{2}-11x+15}dx
(\partial)/(\partial y)(2x+arctan(y^2))
\frac{\partial\:}{\partial\:y}(2x+\arctan(y^{2}))
integral of e^{5/2 x}
\int\:e^{\frac{5}{2}x}dx
integral of xcos(4pix^2)
\int\:x\cos(4πx^{2})dx
derivative of x^3(x-1^4)
\frac{d}{dx}(x^{3}(x-1)^{4})
(\partial)/(\partial x)(e^x*y*dy)
\frac{\partial\:}{\partial\:x}(e^{x}\cdot\:y\cdot\:dy)
derivative of e^{-bx}
\frac{d}{dx}(e^{-bx})
integral of 64e^{4x}sin(4x)
\int\:64e^{4x}\sin(4x)dx
integral of (e^y)^2
\int\:(e^{y})^{2}dy
limit as x approaches 0+of 1/(xln(x))
\lim\:_{x\to\:0+}(\frac{1}{x\ln(x)})
integral of 1/(x^6)+3/(x^2)
\int\:\frac{1}{x^{6}}+\frac{3}{x^{2}}dx
derivative of 2xe^x+e^xx^2
derivative\:2xe^{x}+e^{x}x^{2}
derivative of y=e^{-7x^2}
derivative\:y=e^{-7x^{2}}
derivative of 10^{sqrt(x)}
derivative\:10^{\sqrt{x}}
integral from 0 to pi of e^{-st}sin(t)
\int\:_{0}^{π}e^{-st}\sin(t)dt
derivative of (cos(x)/(2+sin(x)))
\frac{d}{dx}(\frac{\cos(x)}{2+\sin(x)})
(dy)/(dx)=e^{4x+2y}
\frac{dy}{dx}=e^{4x+2y}
integral of ((x^2+7)^{2021})x
\int\:((x^{2}+7)^{2021})xdx
integral from 1 to 2 of (x^2+1)/(3x-x^2)
\int\:_{1}^{2}\frac{x^{2}+1}{3x-x^{2}}dx
derivative of (x+(x+sin^2(x)^3)^4)
\frac{d}{dx}((x+(x+\sin^{2}(x))^{3})^{4})
limit as x approaches-4 of (x^2)/(4x+16)
\lim\:_{x\to\:-4}(\frac{x^{2}}{4x+16})
integral from-1/3 to 1/3 of 1/(1-x^2)
\int\:_{-\frac{1}{3}}^{\frac{1}{3}}\frac{1}{1-x^{2}}dx
integral of x/(\sqrt[4]{x)}
\int\:\frac{x}{\sqrt[4]{x}}dx
integral of sin(x^{1/2})
\int\:\sin(x^{\frac{1}{2}})dx
(\partial)/(\partial y)(xln(y))
\frac{\partial\:}{\partial\:y}(x\ln(y))
x(dy)/(dx)+3y=x^3-x
x\frac{dy}{dx}+3y=x^{3}-x
derivative of e^{-x+1}-x*e^{-x+1}
derivative\:e^{-x+1}-x\cdot\:e^{-x+1}
integral of 14sin^3(x)cos^2(x)
\int\:14\sin^{3}(x)\cos^{2}(x)dx
integral of (5sqrt(x))/(x^3+1)
\int\:\frac{5\sqrt{x}}{x^{3}+1}dx
y^'+2ty^2=0,y(1)= 1/5
y^{\prime\:}+2ty^{2}=0,y(1)=\frac{1}{5}
limit as x approaches 0+of 1/(2x)
\lim\:_{x\to\:0+}(\frac{1}{2x})
integral of (cos(4x))
\int\:(\cos(4x))dx
derivative of (x^3+x^2+x+5ln(5x^2-7))
\frac{d}{dx}((x^{3}+x^{2}+x+5)\ln(5x^{2}-7))
derivative of 8x^{-2}
\frac{d}{dx}(8x^{-2})
integral of (x^5-4x^3)/(sqrt(x))
\int\:\frac{x^{5}-4x^{3}}{\sqrt{x}}dx
inverse oflaplace ((s+5))/((s+3)(s+7))
inverselaplace\:\frac{(s+5)}{(s+3)(s+7)}
derivative of f(x)=2x-(16)/(sqrt(x))
derivative\:f(x)=2x-\frac{16}{\sqrt{x}}
derivative of 6cos(x)+3sin^2(x)
derivative\:6\cos(x)+3\sin^{2}(x)
derivative of 1/(sqrt(2\sqrt{x)})
\frac{d}{dx}(\frac{1}{\sqrt{2}\sqrt{x}})
derivative of 2x+sqrt(x)
\frac{d}{dx}(2x+\sqrt{x})
derivative of x^4-4x^2
\frac{d}{dx}(x^{4}-4x^{2})
(dy)/(dt)+e^ty=9e^t
\frac{dy}{dt}+e^{t}y=9e^{t}
(dy)/(dx)=6y^2x
\frac{dy}{dx}=6y^{2}x
normal of y=x^2-5x+3,(2,-3)
normal\:y=x^{2}-5x+3,(2,-3)
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