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Evaluate the indefinite integral ∫6^x+e^-6x-3/(x^2+1)dx. …

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Wize University Calculus 1 Textbook > Integrals

Antiderivatives of Exponential Functions

4 Activities

Wize University Calculus 1 Textbook > Integrals

Antiderivatives of Inverse Trig Functions

3 Activities

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Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.


More Antiderivatives of Exponential Functions Questions:
Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.
Practice: Definite Integral (~F2017 Final Q26)
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.
Antiderivatives: Exponential Functions
Find the indefinite integral ∫(6x+e−6x) dx\displaystyle \int(6^x+e^{-6x}) \ dx
Exponential Functions: $f$ from $f''$
Given f′′(x)=5ex+2sin⁡xf''(x)=5e^x+2\sin x and given f(0)=0f(0)=0, f(π)=0f(\pi)=0, find f(x)f(x). Enter "f(x)=..."
Indefinite Integrals with Exponential
Compute the following integral: ∫3−x dx\displaystyle \int 3^{-x}\,\text{d}x.
Use upper case CC to denote any constants.
Antiderivatives: Exponential Functions
Which of the following is the most general antiderivative of the function e3x+7e^{3x+7}? In the functions below, cc is an arbitrary constant.
Find ∫(cos7)e3xdx\displaystyle \int (cos7)e^{3x}dx
Antiderivatives: Exponential Functions
Find an antiderivative of f(x)=2e3x−2f(x) = 2e^{3x-2}
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\displaystyle \int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.
Find the equation of the tangent line of the graph y=excos⁡ xy=\frac{e^x}{\cos\ x}at the point where 𝑥 = 0.
Exponential Functions: $f$ from $f''$
Given f′′(x)=5ex+2sin⁡xf''(x)=5e^x+2\sin x and given f(0)=0f(0)=0, f(π)=0f(\pi)=0, find f(x)f(x). Enter "f(x)=..."
Indefinite Integrals with Exponential
Compute the following integral: ∫3−x dx\displaystyle \int 3^{-x}\,\text{d}x.
Use upper case CC to denote any constants.
Antiderivatives: Exponential Functions
Find the indefinite integral ∫(6x+e−6x) dx\displaystyle \int(6^x+e^{-6x}) \ dx
Find the equation of the tangent line to the curve y=23e3−3xy=2^3e^{3-3x} at x=1x=1 .
Enter your answer as y=...
Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.
Higher Order Derivatives
Find a general formula for the nth-derivative of f(x)=e3xf(x)=e^{3x}.
Antiderivatives: Trigonometric and Exponential Functions
If f′′(x)=cos⁡(2x)−x4+exf''\left(x\right)=\cos\left(2x\right)-x^4+e^x, f(0)=0=f′(0)f\left(0\right)=0=f'\left(0\right)
Practice: Definite Integral
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.
More Antiderivatives of Inverse Trig Functions Questions:
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Evaluate the integral ∫x4+1x2+1dx\displaystyle\int\frac{x^4+1}{x^2+1}dx.
Find the value of the definite integral ∫π/6π/3(sec⁡x+tan⁡x)sec⁡xdx\displaystyle \int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx .
Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.
Practice: Definite Integral (~F2017 Final Q26)
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Evaluate ∫−10dx1−x2\int_{-1}^0\frac{dx}{\sqrt{1-x^2}}
Integration Medley
Practice Question
Evaluate ∫x4+1x2+1  ⁣dx{\displaystyle\int} \frac{x^4+1}{x^2+1}\de{x}.
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\displaystyle \int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.
Antiderivatives: Inverse Trigonometric Functions
Evaluate dducos⁡−1usin⁡−1u\displaystyle \frac{\text{d}}{\text{d}u} \frac{\cos^{-1}u}{\sin^{-1}u}. It is not necessary to simplify.
Evaluate the integral ∫x4+1x2+1dx\displaystyle\int\frac{x^4+1}{x^2+1}dx.
Find the value of the definite integral ∫π/6π/3(sec⁡x+tan⁡x)sec⁡xdx\displaystyle \int_{\pi/6 }^{\pi/3}(\sec x+\tan x)\sec x dx .
Find the indefinite integral ∫(11+x+11+x2)dx\int(\frac{1}{1+x}+\frac{1}{1+x^2})dx.
Evaluate the indefinite integral ∫6x+e−6x−3x2+1dx\displaystyle \int6^x+e^{-6x}-\frac{3}{x^2+1}dx.
Evaluate ∫−10dx1−x2\int_{-1}^0\frac{dx}{\sqrt{1-x^2}}
Antiderivatives: Inverse Trigonometric Functions
Find ∫24−t2dt\int_{ }^{ }\frac{2}{\sqrt{4-t^2}}dt.
Practice: Definite Integral
Practice: Definite Integral
Evaluate ∫0319+x2+2xln⁡2 dx\int_0^3\frac{1}{9+x^2}+2^x\ln2\ dx.