What is the integral of 1/(sqrt(7-5x^2)) ?

The integral of 1/(sqrt(7-5x^2)) is 1/(sqrt(5))arcsin(sqrt(5/7)x)+C

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integral of 1/(sqrt(7-5x^2))

\int \frac{1}{7 - 5 x ^{2}} d x

\frac{1}{5} arcsin (\frac{5}{7} x) + C

Solution steps

\int \frac{1}{7 - 5 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{5} d u

= \int \frac{1}{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{5} \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{5}{7} x)

= \frac{1}{5} \cdot 1 \cdot arcsin (\frac{5}{7} x)

Simplify

\frac{1}{5} \cdot 1 \cdot arcsin (\frac{5}{7} x) : \frac{1}{5} arcsin (\frac{5}{7} x)

= \frac{1}{5} arcsin (\frac{5}{7} x)

Add a constant to the solution

= \frac{1}{5} arcsin (\frac{5}{7} x) + C

\frac{1}{1 - x}, i

y = x^{3}, y = x^{2} - 4 x, [- 1, 1]

\int_{1}^{4} (7 x + x) d x

\int (3 x^{2} - 4 x + 2) d x

\int \frac{2}{t} d t

What is the integral of 1/(sqrt(7-5x^2)) ?
The integral of 1/(sqrt(7-5x^2)) is 1/(sqrt(5))arcsin(sqrt(5/7)x)+C