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Popular >

integral of (ax+b)

Solution

\int (a x + b) d x

Solution

\frac{a x ^{2}}{2} + b x + C

Solution steps

\int a x + b d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int a x d x + \int b d x

\int a x d x = \frac{a x ^{2}}{2}

\int b d x = b x

= \frac{a x ^{2}}{2} + b x

Add a constant to the solution

= \frac{a x ^{2}}{2} + b x + C

Popular Examples

derivative of ln(arctan(cos(x)))

\frac{d}{d x} (ln (arctan (cos (x))))

integral of cos(xpi)

\int cos (x π) d x

integral from 0 to 2pi of cos^2(t)

\int_{0}^{2 π} cos^{2} (t) d t

y=2^x+x^2(-1-x)^{sqrt(x)}

y = 2^{x} + x^{2} (- 1 - x)^{x}

integral of 2cos(x)e^x

\int 2 cos (x) e^{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (ax+b) ?
The integral of (ax+b) is (ax^2)/2+bx+C